The feat lets you swap out a power for a power you could have taken instead. Sort of like instant (temporary) re-training. You pick the power you're swapping /in/ when you take the feat. The power you swap out must be the same level. It's like a very limitted version of the Wizard's spellbook, really.
You get no choice of level 20 daily, and it's a PP power, not a class power, and it's not the same level as a level 19 Fighter Daily (assuming the power you picked for Martial Adaptation is a level 19 daily).
(hmm... if this feat is worth taking - if it's realy 'worth a feat,' then the wizard's spellbook is worth at least 3, just for the ability to swap dailies, nevermind utilities - and really nevermind the Mage's spellbook... Interesting.)
tl;dr: No.