Looping back to the train vs plane discussion earlier in this thread, I would almost always prefer to take a train over a plane but this is one case I'd probably take the connecting flight. Normally the last thing I want to do getting off a redeye TATL is to wait around an airport for an hour or two and then get on a cramped A319. But, much of the inefficiency of air travel (getting to remote airport, clearing security, etc.) is not applicable for connecting flights.
If I was standing in Frankfurt city center and going to Berlin, I'd take the train every time, even if it were more expensive. If I'm standing airside at FRA and have a protected connection to an hourly flight, the calculus changes, especially if (like with award travel) the price is the same.
However, there are times I have (and would again) connect to a train. Price is a big motivator. There are many times when e.g. an LAX-FRA ticket + train ticket is way less than LAX-FRA-TXL ticket. If it's $700 r/t to FRA [in Y] and $1400 r/t to TXL via FRA, to me it's a no-brainer to take the train unless I'm on a super tight schedule. I usually go to Europe for 3 weeks at a time so 4 hours on the train direct to city center vs 2 hours boarding, taxiing, flying, taxiing, and finding transit to city center doesn't make a huge difference. I can use my phone, use my laptop, eat a sandwich, look out the window, and arrive unfrazzled.
With the Rail & Fly it's only EUR 33 for an unrestricted train ticket anywhere in Germany:
Rail&fly with United in Germany