Mosel Valley (Cochem or Trier) or West Rhine Valley (Mainz) for 3-4 nights

"I have heard of the beautiful Rhine valley forever, but more recently have heard that it has changed and the Mosel area is more picturesque & romantic and less heavily commercial/touristy."

Nothing has changed. The Mosel has always been quieter. The Rhine has been a major transportation artery for centuries - barges, cruise ships, passenger trains, freight trains, cars, and at some times of year bicyclists put the Rhine in perpetual motion. The only small recent change has been the addition of a high-speed rail line between Frankfurt and Cologne that REROUTED some passenger traffic away from the Rhine. The Mosel is a shipping lane as well but not nearly as important as the Rhine. You will see barges there as well, but fewer.

"...the Mosel area is more picturesque & romantic..."

Depends on how you define those terms. The Rhine is totally cluttered with castles between Mainz and Bingen. They are much less prominent on the Mosel. So if castles = romance, the Rhine wins. Trails like this one near Bingen offer incredible scenery in all seasons:

http://www.michaelleukel.photography/images/gallery/ML-11048-Winter-3_1458122215.jpg

OTOH the Mosel is a smaller and much less forceful river - it meanders endlessly, almost turning around and back into itself in spots. I find those parts of the Mosel extremely picturesque and romantic:

https://upload.wikimedia.org/wikipedia/commons/7/73/Moselschleife_Bremm_0014a.jpg

https://upload.wikimedia.org/wikipedia/commons/c/c1/Panorama_Prinzenkopf_-_Bullay_-_Marienburg_-_P%C3%BCnderich_2010.jpg

Also, there are parts of the Mosel where trains do not venture at all - so the setting is somewhat more natural, less manhandled. Of course, that's not so great for train travelers. The Rhine has trains on both sides, making it the easier river to explore fully, if you were so inclined to do so, without a car. Trains don't make the Rhine "industrial" IMO - but there ARE some places, mostly north and south of the Bingen-Koblenz Rhine corridor, that are heavy with real industry. On the Rhine, I'd focus mostly on the Bingen-Koblenz segment.

Touristy: The Rhine towns get lots of tourists but most are NOT heavily touristy. Stay out of Rüdesheim if you want to avoid "touristy" - it's a tour-bus stop. Cochem on the Mosel is a tour-bus stop too - but honestly, the place is so incredibly attractive that a crowd of tourists doesn't detract, IMO. I've stayed there half a dozen times.

http://www.der-takt.de/typo3temp/_processed_/csm_NEU_T_Reichsburg_Cochem_3_087e83a8d1.jpg

"We will not have a car and would like to be well located for traveling around within which ever area we choose."

I'd suggest staying in Boppard or Braubach on the Rhine (both are just south of Koblenz, the train hub town for the area, but not a place that's romantic at all IMO.) That way you can stay in an attractive small town and visit both rivers easily by train. I see no reason at all to choose one river over the other as both are wonderful. Braubach is very small but also the home of Marksburg Castle, the best Rhine castle to tour. Boppard is larger with lots of room and restaurant choices.

Cochem is a good town to base in if you're visiting only the Mosel (again, just for emphasis, that's a mistake IMO.)

As always, terrific advice from Russ. I would add that Cologne is not part of a visit to the Rhine Valley. It's an essential historical and cultural city, with more magnificent museums than you can find time to visit. There is no real river scenery within reasonable boating distance of Cologne. The "Rhine Valley" for tourists ( ... sorry ... ) normally means the Middle Rhine. The most frequently recommended boat ride is (conceptually) from Bingen to Boppard or St. Goar. All other Rhine travel should be by the much faster and frequent trains. (Even if you have a car, since the car can't follow the boat without a driver.)

I'll go a step farther and say that the scenery on the Mosel is pretty but "boring". I don't recommend boating the Mosel, but a drive (say, from your pretty sleeping town to Trier for the day) can be very scenic. The river itself is not remotely like the Rhine. The shipping on the Rhine is a detriment to waterside hotel rooms - NOT a detriment to tourist views from a KD boat on the Middle Rhine.

Whenever someone writes "picturesque and less heavily commercial touristy", I think they are deceiving themselves. The opposite of the "picturesque and touristy" is, today, "postwar reinforced concrete single-family homes on redeveloped roadways." You are not going to stay in a lovely, deserted, quiet wooden village from Band of Brothers. Even on the Mosel, you have to make appointments for the best wineries. Sure, maybe you can get a vacation cottage in the woods. But that's not a hamlet of authentic German culture. It's a rural escape.

Although 25 days is a reasonable amount of time, it's a vast amount of travel time to "see all of" Germany in one trip. Between business and vacations, I've been to Germany six or seven times. I have a lot more to see. It is a varied and rewarding country. Even in 25 days, you will be missing as much as you see-that's unavoidable.

Thank you, both. Russ, I will be checking out those links. This is just the information I needed.

And, I wasn't thinking Cologne was in/near the river valleys. I just used some confusing punctuation.

Susan, I've traveled through both river valleys several times. If it is your first trip to this area and you have a car you can see a bit of both. The time to drive between the Rhein to the Mosel is much longer than you might guess from the map, though. The roads connecting them are pretty narrow and winding. BTW: Even with a car, I'd take the train to Trier. The Länder Ticket is such a great deal in Rheinland/Pfalz.

Thank you, Dutch. Do you think 3 and 1/2 days in this area (without a car) is too much time? We could add a day to Munich or Cologne visits. . . or to the end of our trip (currently 6 days) in Paris. Susan

I thought that the Mosel Valley was prettier than the Rhine. But the Rhine has a lot more going on and better access. The Mosel Valley is really best seen from a car. Is there any reason why you would not want to rent a car in Cologne for a couple of days? If this is acceptable to you I would drive from Cologne up one side of the Mosel Valley (to Cochem) and back along the other side. Visit Burg Eltz if you are interested in seeing a castle - it's one of Rick's favorite castles. I would see the Rhine by river boat. You could get off in St. Goar, have lunch and catch a later boat back to Cologne. This is essentially what we did in 2010 and it worked out very well.

"I would drive from Cologne up one side of the Mosel Valley (to Cochem) and back along the other side."

Just to be clear about the train alternative... it is precisely this stretch of the Mosel that the train line covers inch by inch; the train hugs the river the entire way. Upstream from Cochem, the river becomes too curvy for train tracks to follow - it is this part that a car is helpful for exploring if you wish to stick to the river the whole way. Check this map with train line in red, Mosel River in blue.

Mosel train scene

Just to be clear about the train alternative... it is precisely this stretch of the Mosel that the train line covers inch by inch; the train hugs the river the entire way

I guess it's more a question of the way I like to travel when sightseeing. The train may be covering the exact same territory, but in the case of a very scenic area like the Mosel Valley I thought that the OP would like to be able to stop whenever a photo-op or a potentially appealing lunch stop appeared out of the window. It is tough to get the train to accommodate what might be a once in a lifetime opportunity. If the train and road are paralleling each other in a flat desert it would not really matter what form of transportation one took. In fact a train or plane would probably be preferred by most people.

"Do you think 3 and 1/2 days in this area (without a car) is too much time?"

I do not. No way could you begin to exhaust the possibilities.

I previously posted a few Rhine options for the area south of Koblenz for you on your other thread. A few more there:

Rhine Castle tours: Marksburg (Braubach) - Rheinfels (St. Goar)
Rhine Cruise: Bingen to St. Goar, 1.5 hours
Excellent Open air museum in Bad Sobernheim (train outing from Rhine base)
Rhein Castle Trail (Rheinburgenweg)
Rüdesheim

The Rhine north of Koblenz:
Remagen's WW II museum
Nice riverfront eateries in Remagen like this one and this one.
Linz am Rhein

The Mosel:

Reichsburg (castle tour, Cochem)
Cochem Winery, near station
Walk through the woods to Burg Eltz (castle tour)
Mosel Cruise: Cochem to Beilstein, 2 hrs. round trip
Trier
Winningen, wine town

You can reach all these places by train. Day passes are inexpensive and provide hop-on, hop-off travel flexibility:
The Rhineland-Palatinate ticket covers everything - €29/2/day. (VRM day passes are cheaper and cover Oberwesel and north on the Rhine, Koblenz to Cochem and Bullay on the Mosel.)

"I guess it's more a question of the way I like to travel when sightseeing."

Yes, I get that. That's how we usually do it, it was very enjoyable, we were able to make impromptu stops as we go for any length of time we wish... the train runs on a schedule that's less convenient. Of course, there are offsetting advantages for train travel that could be enumerated... the peril of hitting wineries and hopping back behind the wheel, just for one... But the main thing is that susan has repeatedly been firm about not having a car.

I can't comment on the ease of getting to these places by train as we have friends living in Germany that drove us around. However, our trip to Burg Eltz was magical. A beautiful hike through the woods and a wonderfully restored/preserved castle. It lived up to the expectations RS set! We also really enjoyed Cologne. Took a tour of the Cathedral and caught a free organ concert later in the evening. We also visited the Roman History museum near the cathedral, which was really interesting.

Mosel is better by far. If you stay in Trier don't miss the archeological museum "Landesmuseum Trier" http://landesmuseum-trier.de and the great ethnological and open air museum Roscheider Hof http://roscheiderhof.de .

These replies and the discussion have been very helpful. Thank you all so very much. Susan