I have owned many Boogie rigs including a few Triaxis rigs (still do).
Both the Stereo 2:Fifty and 2:Ninety sound significantly "bigger" with the Triaxis than the 20:20... EL84 tubes don't have the same presence as you get from 6L6 power tubes. I'm not saying you won't have a great sound, but with the 6L6 power amps you'll have a better sound.
The 2:Fifty is a nice middle ground -- not as heavy as the 2:Ninety, and not as loud. That said, all of these amps, even the 20:20, are more than loud enough to drive one or two 412 cabinets.
BUT... with the 2:Ninety, you get additional features that significantly impact your tone -- the Deep and Modern voicings in the POWER AMP are only achieved if you've got the 2:Ninety. ALSO, the 2:Ninety has a half-power mode of operation, which the 2:Fifty does not. NOTE: The OLD 50:50 power amp had a half-power mode, but it's not as good sounding as the 2:Fifty that replaced it.
So... no, you don't need a different power amp, and I'm envious of the super light weight of a 20:20, but there is a significant tone difference. And you don't have to have the power amp cranked to hear it.
Scott