Taking a train vs. renting a car.

Connections are not generally difficult unless you are carrying too much luggage.

https://www.ricksteves.com/travel-tips/packing-light/packing-smart

There are so many things to see and do within several miles of Bacharach that Day 1 (which can be iffy when you're jet-lagged and drowsy - and shouldn't be driving btw) + Day 2 probably isn't enough time. You probably would do well 3 days/nights here. Nearly everyone that reads Rick Steves seems to think the Rhine is just for a river cruise... and that Füssen is "castle country." But that title goes first to the Rhine.

http://www.loreley-info.com/eng/rhein-rhine/castles.php

You're sort of missing out if you don't make time for visiting the castles there (Marksburg, Rheinfels, Burg Eltz for starters, all of which have histories of around 1,000 years behind them) not to mention the nearby towns (Boppard, Oberwesel, Braubach, St. Goar, Rüdesheim. The Füssen area "castles" that everyone visits are much younger palaces (Neuschwanstein barely a century old) and played a very different role in European history (Neuschwanstein almost no role at all - poor King Ludwig moved in before it was finished and died 6 months later, and then the tourists started swooping in.)

I would subtract a night from Rothenburg. You could leave Bacharach early on Day 4, arrive in the early afternoon in Rothenburg, spend the afternoon evening and night there, sight-see in the morning of Day 5 if you missed something, then proceed to Munich in the afternoon.

There is no one answer, other than peoples opinions. Have you ever traveled in Europe before? If not, its hard to explain how rail travel makes things easier than touring by car. All your destinations can be reached by train, which eliminates the hassle of parking and the stress of navigating, etc. Some people enjoy driving so if you want that experience go for it. But for me, I'd rather ride a train than have the stress of driving. The highways are not much more scenic than in the US.

Connections are like transferring buses in a US city, not like airline connections. They're timed to be doable.

I see five days of travel for your entire trip: Frankfurt to Bacharach, Bacharach to Rothenburg, Rothenburg to Munich, Munich to Hohenschwangau day trip, and Munich to MUC. In Munich, a rail pass would cover the S-Bahn to the airport, but not any other transport (U-Bahn, trams, or buses) to get to/from the S-Bahn.

For Frankfurt airport regional station to Bacharach you can purchase two RMV (Frankfurt metro) tickets at the airport station for 12,20€ each (24,40€ total).

For Bacharach to Rothenburg, you can get a Savings Fare, advance purchase ticket online. For a lot of dates, I see 55,80€ tickets for two with three or four changes. Connections are at least hourly. Most trips take 4¾ hrs. Even without the advance purchase, Bacharach to Rothenburg for two people is only 128€.

For Rothenburg to Munich and for the day trip to the castles, a 31,-€ Bayern-Ticket each day would suffice. The Bayern-Ticket would include the bus from Füssen Bhf to Hohenschwangau, but a rail pass would not. Oh, well, the bus costs only a few euro per person each way.

And, finally, anywhere in downtown Munich to the airport would be 11,60€ per person (23,20 € for two).

You don't want a car in Munich. Parking is expensive and MVV fares are low. You might spend more for parking than you would to use public transportation. An all day pass for two (up to 5, really) in the innerzone of Munich costs 12,80€.

So, I get a total price for five days of travel using the trains of 165,40€. RailEurope charges $450 (about 390€ at today's exchange rate), so a 5-day German Rail Twin Pass is at least twice what you should pay for Bahn and local tickets. Even without the Saver Fare, point-to-point tickets are only 237,60€, so you'd still be $175 ahead.

As for renting a car, ViaMichelin estimates the gas alone for a compact car for your trip at almost 100€, so where are you going to rent a car for $75 a week?

So, I think you can see that the trains in Germany with point-to-point tickets beats either a rail pass or a rental car. And, besides, in this country to get almost anywhere, you have to go by car. Using trains is something you cannot experience here.

I am a major fan of the DB so I would take the train over renting a car any day. Taking the train is something we do daily so for us it's great fun taking public transport when we're in Europe.

If those are the only places you’re going, and can be reached by train, then take the train. If you plan on any side trips en route, then rent a car. I wouldn’t have a car in either Munich or Frankfurt, but would be fine for the in between places.

Car is handy for Burg Eltz visit from Bacharach if you are interested in that (highly recommended). Otherwise visiting there and back will eat up a lot of your one day (not counting day of arrival). I am assuming you are going straight to Bacharach, not clear if you are overnighting in Frankfurt for one day. With a short itinerary Bacharach to Rothenburg long train ride might not be optimal. A car would save you time, but only a couple of hours though according to rome2rio.

A train pass, if you mean a multi-day country pass, is unlikely to be economic. You can travel fairly cheaply from Rothenburg to Munich on a regional day pass. Within a provence in Germany, these are generally a real bargain. The Bacharach to Rothenburg leg, you can probably save by buying in advance. Trains in Germany run on time as you might expect, but many transfers some with opportunities to miss connections. I don't know if I would choose car over train just because of that though.

Germany is actually one of the easier countries in which to drive in Europe, just stay out of the left lane unless passing.

You did not ask about this, but if the flight is not already booked, I would consider narrowing your geographical coverage. Not a huge fan of Munich here, great museums but overpriced for hotels and often very mobbed by fellow tourists.

With only one full day (2 nights) in Bacharach, I would not recommend spending it on Burg Eltz. There are just too many other things to do and see in and around Bacharach. Assuming you are not doing a Rhein cruise, take the train to St. Goar and explore the Rheinfels castle ruins, then take the ferry across the river to St. Goarshausen and the train (21 minutes) to Braubach to see the Marksburg (English tours at 1 and 4 PM), one of two castles in the area (Burg Eltz is the other) that was not destroyed and rebuilt.

As for Bacharach to Rothenburg odT, the trip by rail can take as little as 4¾ hr. The trip by car can take as much as two hours less (assuming no missed turns, traffic tie-ups, etc), but that doesn't take into account the time to pickup and return the rental car. And, I can't find rental offices in either Bacharach or Rothenburg, so using a rental car from Bacharach to Rothenburg probably means picking up the car at FRA when you arrive and returning it in Munich when you get there - five days of rental charges for only needing the car for 3 hours.

There is a Bacharach to Rothenburg connection leaving Bacharach at 10:06, taking 4¾ hours, and costing, with advance purchase, as little as 55,80€. It has three changes: Mainz, 46 min; Würzburg, 9 min; and Steinach, 13 min.

We were stressed about figuring out the trains and tickets in Germany and rented a car. There were also 3 of us and large suitcases, so it seemed like the right thing. Most hotels charge for parking, gas was pricey, and many highways were under construction.

Most hotels charge for parking, gas was pricey, and many highways were
under construction.

That sounds lightyears more stressful than picking trains and buying rail tickets.