Well, Class D is the rage right now because it is very efficient (i.e. loud) in a light-weight package.
It's actually getting harder and harder to find powered speakers that aren't Class D these days. Everybody seems to have jumped on the Class D bandwagon.
But, as I said up-thread, they have a history of being somewhat less than musical in the top-end department.
They're fine for bass players and jazz guitar players though.
The newer Class D amps, eg. in the QSC K series, are probably a bit better in the top-end department than the older Class D designs (eg. Acoustic Image's original amps).
But my own experiences when renting K10's and K12's weren't so good as far as the top-end is concerned.
I was running an older and brighter version of the Axe's firmware back then though.
I plan on renting some K series speakers again to try out with version 10.3.
I love the idea of playing FRFR but have as of yet not been able to get it to give me the same buzz as playing through a real guitar cab.
Generally speaking, to the best of my knowledge, Class A/B has been the standard for hi-fidelity power amps for many years now.
So if you can find a way to power the Axe with a hi-quality Class A/B amp that fits your budget and form-factor needs you'll probably be able to achieve a more sophisticated sound from the Axe.
[Of course a well-designed Class D amp will sound better than a poorly designed Class A/B amp.]
I've ended up with a Bryston 2B-LP-Pro that I bought for $400 used. They're very expensive new though, prohibitively so.
I use it in bridged mono mode, for 200 watts @8ohms, driving an EVM-12L (guitar speaker - not FRFR) in an open back cab, and I couldn't happier with my sound.
The Bryston sounds markedly better than every other power amp I've tried with the Axe. (Pearce G2r power section - bridged or un-bridged, ART SLA1 - bridged or un-bridged, ART SLA 2, QSC PLX1104, Yorkville AP-Series, Mesa Simul-Satellite power section - Simul-Class tube amp - like 1/2 of a Mesa 2:90, etc.)
I've been told that power amps don't get any more transparent than the Bryston products.
Sometime soon I'd like to try the 2B through an FRFR passive cab, but I think I'd be under-powering most cabs of this ilk.