BAT VK 250 vs Pass XA30.5 for Wilson Sophia 2

Any experience with either of these amps on Sophia's?
Have them about 2 weeks now and they are terrific with my Rogue 90 tubes.
I'd like a balanced ss amp as the rest of my system is balanced (Mytek Brooklyn dac and Vincent Sa-t8 tube preamp).  Room is 18'X13' and primarily classical listening, especially symphonic.
What are the shortcomings of the rogue tube amp with the Sophia's that are making you look at SS?
I like the Rogues and will keep them - I like to have a tube amp around to switch to when I get the itch for a different sound.  They are very musical but don't have the grip on the bass or treble detail that I know the Wilson's are capable of.
I would like to stay under $10,000 and utilize the balanced capability in the rest of the chain. 
Ah, I see.  I asked as I have the same speakers, and a 100 watt tube amp.  I was curious if there was something I may be missing.  Perhaps there is, if I were to compare to a very powerful amplifier, but so far, a month in with my Sophia 2's, I am happy.

A couple of years ago I compared a 250 watt Pass Labs solid state amp (model X250) and solid sate preamp (model xp-20), in the same price category as my Audio Research VT100 mk II power amp and LS-25 mk I line stage.  I wasn't using the Wilsons at the time, but I was toying with getting away from tubes.  Despite the larger amount of power, I sold the Pass Labs gear and kept my ARC gear.  It just sounded so much better that the comparison was quick and easy.  My wife looked at me during the AB tests on the sofa and told me, "you'd be crazy if you sold the tube amps... they sound way better!"

I know this is not the perfect placement for this story, as your situation is different from my ARC vs PASS experiment, but perhaps it is useful in some way.  Good Luck!  I'd be very interested to hear what you purchase and what you feel about the improvements in the Wilsons with a more powerful amplifier.

I suppose if I were in your shoes, I would put the Audio Research solid state amps such as the DS 450 and amps from Balanced Audio Technology on the list of gear to listen to.
You can get a used BAT VK-600SE for, at most, 1/2 of your budget.  A very powerful and very good sounding amp. 
Both great amps and would place the Pass in a little higher league. As was commented on previously you might look at a good used ss. I have both an ss and tube pre to run with my ss amp. I love the mix of tubes and ss and with larger speakers like the wilson or my b&w's they can run fine on lower power but as you mentioned the grip, dynamics etc really shine when you have some 'good' power. The new ss amps offer all the finesse etc you might want. Also as was previously mentioned the ARC gear is very nice, particularly their new stuff.
I don't have the Wilson speakers but did switch from a Rogue M-180 to Aesthetix Atlas Signature about a year ago and really liked the change. The Atlas is a 200/400 WPC into 8 and 4 ohms respectively, highbred amp with tube input and solid state output. New or used within your budget.