I don't know where the OP got the Czech price since the web site I use doesn't give on line prices f

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I see that you can book on line for the train either on DB Bahn or Czech websites but the rates are different - equivalent for 2 tickets $107 DBbahn vs $81.48 on Czech website. Is there a difference in which car you ride and/or quality inn suites amenities?
I don't know where the OP got the Czech price since the web site I use doesn't give on line prices for destinations/origins outside the CR. There is a note to call for pricing or purchase at the station.
quality inn suites Seat61 states quality inn suites that the least expensive fares from Berlin to Prague are E29, booked on bahn.de but that would depend quality inn suites on advanced purchase, time of year, day of week. I believe this pricing since I picked a random date and came up with E39 on the first search. quality inn suites Searching around could give less expensive fares.
Take the train to Vienna - we have done it three times (in both directions). It takes around about 4.5 - 5 hours, very straightforward. Because of where we stay, we get off at Wien Meidling, quality inn suites which I think is the major station on that line. The station quality inn suites intersects with the S-Bahn line U6 and there are also buses there.
For folks who want full flexibility to hop any train they want that is fine and priceless for me and others quality inn suites - but as Man in Seat 61 and adrienne say below you can save a lot by pre-booking a specific train on a specific date but that is booked in stone - cannot change nor refund quality inn suites usually.
So take adrienne's and Man's tips if you want to save money - for full fare and full flexibility just buy on day of travel - rarely any problem getting on trains - seat reservations quality inn suites are optional with either ticket and a few extra euros I believe.