Car vs Train

It is hard to decide when plans are so unsettled. If not having a plan is causing stress now, then it probably will continue to do so.

You can book a rental car for a month and be pretty sure of that fixed cost, with fewer variables based on where you drive, although gas will be a variable, and highway tolls in France are based on distance. Parking can be expensive in big cities, as well as most of us avoid driving at least in Paris, and probably other big cities on your list, as well. Driving longer distances does take energy on the part of the driver, more than sitting on a train.

Trains serve your destinations and there is no deadline to buy train tickets, but they can add up. Rick’s Train Travel Time & cost Map gives you an overview of faster train travel times in hours, as well as regular (full-price) 2nd-class fares, which you'd be more likely to pay on short notice.

For train travel in more than 4 countries, a Eurail Global pass gives you a large amount of freedom, but not in France, where your longer trips must be reserved ahead (and reservations for a direct TGV Lyria to/from Switzerland are expensive). So Paris brings up issues for either car or train. Cheaper passes require naming a maximum of four specific countries.

Mixing some car rental and some train travel is also an option, but you're more likely to get the size and price of the car you want by reserving ahead for specific dates.

Edit: Do you only have two weeks? I thought it was longer.

I find a car stressful, especially with many big cities in the mix. Navigating, parking, traffic, feeling like a rolling road block on the autobahn, filling the fuel tank (OUCH!). It will do you no good in the Berner Oberland.
Train station is right at the airport. Get your luggage and go. No waiting at the rental counter, locating the car in the garage, going over it and taking pictures of it to make sure there are no dings they are going to try and stick on me. Oh and insurance.
The train has its own set of problems, but while you are driving white-knuckled down the highway, I'm sitting in the bar car sucking on my first cold German beer.

Yes, cars are stressful and a lot of work. They allow you to get off the beaten path out into the countryside, but it doesn't sound like you're doing much of that (except Normandy area). In Europe, the train is going to get you almost everywhere you want to go, and as noted it's so much more relaxing and allows you to sit back, look around and meet some locals.

If trains go where you want to go (check the German train website for schedules from all over Europe), take the train.
If trains don't go where you want to go, rent a car.
For example, in Europe (different from here) if your destination is a big city, and trains go there, you'll lower the stress level, and increase your enjoyment, if you take the train.

The worst thing I can think of about driving a car on the highways of Europe is getting back home to the States and having to share the road with drivers that don't keep in the slow lanes and are oblivious to the courteous rule that the fast lane is only for passing.

Some good things about driving in Europe are: honing your parallel parking skills, buying a good bottle at a winery and not having to drink it before packing up to schlep your stuff off to the next town, not being too terribly worried if your socks didn't dry the night before because they can drape in the back window instead of being stuffed in your bag before you head to the train platform, and most important for me, you can enjoy a piece of tender fruit as a lovely snack, even though it took four days to fully ripen.

A well-packed car is your own rolling butler's pantry!

For each leg of your trip, ask yourself, which is more important, the destination or the journey. If the former, take a train, if the latter, go by car.

I like trains and cars equally and view them simply as tools to suit my travel needs, not as ends in themselves. Like a lot of folks here, my wife and I use trains between cities in Europe, but when we want to get out into the countryside, I rent a car. For our upcoming trip, also in May and June, we plan to use trains to visit Munich, Nuremberg, Prague, Dresden (three nights each) and Erfurt (two nights) over a two-week span. Upon leaving Erfurt, we will pick up our rental car and spend the next two weeks in the Bavarian countryside.

It's a shame you didn't get flights into one city and out of another--open jaw. Backtracking to Frankfurt is expensive and it'll cost you a day of travel.
You might want to get on Mapquest or GoogleMaps and plot how far it is from city to city. I think you'll realize your planned itinerary is virtually impossible to make in the 2 allotted weeks.

You could do probably visit Berlin, Prague, Salzburg and Munich traveling by trains.

Or, you could take in Munich, Salzburg and drop south into the Austrian Alps (Tirol) to get your fix of the incredibly beautiful mountains.
You should save Budapest, Paris and Switzerland for your next trip as they're worthy of more time than you have.

Some thoughts:

1) As Rick has said in his books, the cost break over point is three people for car vs. train. Remember, when you ride on a train, you are basically renting it. For three people you are renting it three times while you only rent the car once. It's too bad your timing is too short to do a lease program which is the slick way to travel by car in Europe.

2) Driving in Europe is a piece of cake as long as you stay out of the big cities assuming you are a competent driver. In the big cities either you park on the fringes and take a commuter train in or go in park and it and sight-see on foot. We have done both. The worst part of driving on the continent is coming back and realizing what a pile of crap our highway system is.

3) I'm planning for our September trip using Google maps and just for chuckles I looked at the train travel times for some of the places we want to go and found that trains come with a huge time penalty in many cases unless you are just going from one big city to another. The time and route flexibility of driving is unbeatable. Doing the Berner Oberland without a car is unthinkable unless you have all the time in the world. Also, your car will never leave you behind just because you were one minute late betting back to it.

For a fuller discussion of trains and cars, you might want to look at the much longer discussion earlier this month that covered the pros and cons of each in a lot of detail.

Righto...driving in Europe is a piece of cake until you caught in the ZTL zone or speeding on that wonderful autobahn or have to fill up on petrol at $4 per LITER (not gallon) or hunt and pay for that non-existent parking spot or pay tolls every 15 feet in Italy and France or shell out $50 for a vignette in Austria and Switzerland or put a $10 scratch on the trunk that turns into a $2500 bill from Hertz or... the list goes on and on and on. If you want relaxation and enjoyment then buy some cheese, fruit and a nice bottle of wine to consume as you zip across the rails at 100 mph.

I'll let you in on a secret, too...you can even get to out-of-the-way places too. Switzerland's Post Bus, for example, goes to the most remote villages you could ever think about visiting.

If you just must absolutely sit behind a steering wheel to have fun then by all means go for it. Otherwise hop on the train and let the conductor do your driving for you!

yes, different horses for different courses. Another consideration is, do you like driving in the first place? Because if you don't, it's not much of a vacation if you're in a car. And frankly, how comfortable are you behind the wheel? Because when you're driving you're also navigating, and that's a lot of work. and the folks in Europe drive like the folks on the East Coast. So if that concept scares you, don't drive.