Vienna and Prague in December

Presumably you have your roundtrip air already booked to Prague? If not, what would be better is if you could get an "open jaw" flying home from Vienna, rather than backtracking to Prague. But if you do need to return to Prague, I would go to Vienna as soon as reasonably possible after you arrive and do that city first, then return to Prague for the last few days there. The reason I recommend that is that you do not have much time for this trip, and if you fly back to Prague, you would either need to do it the same day as your flight home, which is very risky (if your flight to Prague is delayed, and you miss your flight home, if it's a separate ticket you would probably have to buy a new full fare ticket home), so you'd need to come the previous day, which splits your Prague stay and you lose a Vienna night.

We do have round trip tickets to Prague already. I was worried about that. But I’m a little worried that going from Vienna to Prague could be a slight letdown. And I don’t want our experience in Prague skewed. I say that because my understanding is that Vienna is big and grand whereas Prague is very quaint with a small old town area. What do you think?

I think a flight is a silly idea and that you should take the train.

I honestly don't think it matters much which one you experience first, so I would go with what is most logistically convenient. They're both big capital cities, but of rather small countries, with a lot of architectural beauty. As Vienna was the capital of a great empire, and Prague a provincial city in that same empire, the former has quite a bit more to see in terms of art, museums, palaces, etc. (and in December weather, having lots of indoor things to do is good) -- but I think that goes more to how you divide your time between them based on your interests, than the order of visit. There's plenty to see in Prague as well.

Fast trip, or slow trip, train or plane its all good if you enjoy it. Nothing is silly except the inappropriate.

So, what could it look like.

Saturday: Leave the US
Sunday: Arrive Prague about 2pm jet lagged. In hotel by 3:30pm
Monday: Prague
Tuesday: Prague
Wednesday: half day Prague and late afternoon train to Vienna arrives in time for bed
Thursday: Vienna
Friday: Vienna
Saturday: Fly back to Prague late flight cause you didn't buy open jaw tickets
Sunday: Fly home.

Alternate: if you can find a flight from Vienna to Prague that gets you into the airport 4 hours prior to your flight to the US, then do that on Sunday. Why 4 hours? Cause with separate tickets you will need to recheck bags and go through security again and if your flight is late you loose your flight home.

As for Prague being "quaint" . Thats a matter of opinion. To me its a very, very, very lovely worthy to be seen and experienced but overcrowded and over priced tourist trap. As for Vienna being intimidating. For me Vienna, or the parts that tourists go to see, is a museum city. Majestically restored and put on exhibit (dead things under glass). Okay hyperbole on both counts, but sort of my personal impression.

Now, Budapest around the edges is as magnificent as Vienna, in the pockets it can be quaint like you are hoping Prague will be, but in the whole it is a town you wear like a comfortable old pair of jeans. Easy and very cheap 1 hour direct flights to and from Prague on M/F/Sat 3.5 hours with one stop the rest of the week.

Saturday: Leave the US
Sunday: Arrive Prague about 2pm jet lagged. In hotel by 3:30pm
Monday: Prague
Tuesday: Prague
Wednesday: half day Prague and Lufthansa 4:45pm flight to Budapest arrives 8:20 pm (<$150) transfer to hotel and then hit a wine bar to wind down.
Thursday: Budapest
Friday: Budapest
Saturday: Fly back to Prague Ryan 7:00pm flight to Prague (<$100) arrives 8:15 pm
Sunday: Early morning flight home

How quickly do you adjust to jetlag and do you want a mid-trip break one day?

I like to immediately jump on a train after I arrive in Europe when I am doing a multi-city round trip via train. You have to do some walking to get to the train and you delay your arrival at a hotel by a few hours or more (both good for adjusting to time change IMHO). So, I would head straight to Vienna from Prague.

Then, it becomes a question of how and when to get back to Prague. You can fly, as suggested, or travel by train. I prefer morning trains as it gives me time to reflect on where I have just been, including Istagram posts or emails using the onboard wifi and time to think about, plan and download apps for what I will do in the next city. Upon arrival I head to my hotel to drop my bag or check-in and begin seeing the sights. BTW the scenery out the window between Vienna and Prague is nice, but not outstanding. Some farm country and small mountian (big hills) valley views.

I thought Vienna felt like a smaller Paris, FWIW. Especially the northern part of the Ring where I was staying.