D'Agostino vs. Ayre

The Dags are amazing with the Wilson line. Great liquidity and system synergy. Almost tube like but still has tremendous grip. Ayre is a great company and the Ayre MX-20 amps are great with Wilson, but the Dag/Wilson combo (for speakers Sasha and above) has that certain Je ne sais quoi that must be heard to be appreciated. I had the Dag stereo amp in house with Sashas a while back and they were simply the best American made ss I have ever heard with Wilsons. I've heard great things about DartZeel, Gryphon, Tenor and Soulution among others with Wilson, but do not have first hand experience with those combos. 

Knowing now you are powering Alexias the D’ags are the clear choice over the MXR-20s.
If you want them to sing and dance for their supper then high powered tubes are essential.
VTL Siegfrieds or ARC 750 SEs are the best matches for Alexias I’ve heard so far.
Just heard the Boulder 2160 with Alexias recently which was revelatory so I reserve the right to equiviquate and retract previous musings with unassailable certainty.

Is there a significant sound difference between the D'Agostino Momentum stereo amp, the S-250, and the mono 400s? As efficient as the Wilson's are, they don't need a ton of power to sound good.

Agree with khrys on tube choices but will note that the ARC Ref 250se works well with Alexias as do VTL S400. More power is better but there is a cost-benefit analysis to be done.
I've only heard DAG monos on Alexias but the Dag s 250s were in house with my Sashas and I felt that they didn't break a sweat. Call Dan at the shop and ask him what the difference will be. I'm sure he will be straightforward in his response. 

Can't speak to the sound, but if you're considering spending this kinda coin, you should also be concerned about support and service.  I have an Ayre product, and when I called them, they coldly told me that they had dealers to deal with questions from their product owners.  Never again will I buy an Ayre product.  Life is just too short to deal with arrogant dik-heads.