Musician vs. audiophile

In general, Wilson speakers sound great when... they are properly matched to other components, proper cabling, and pretty good to great acoustics (and positioning) in the room.  If they sound flat and uninteresting it is not unusual at all.  However, this is the 3rd iteration of Sophia's and they should (normally) be the cornerstone of your system.  A Wilson dealer should come over and see and hear your system and make some suggestions starting with the most cost-effective ones 1st.  If you can afford a more forgiving pair of speakers there are several i can think of, but that could involve a lot
of money, time, and effort as well.  I always wanted the accuracy of Wilson's but i thought i could do better elsewhere and for less money and ended up with a giant-killing pair of Eggleston Andra's.
Anything similar to those would IMO add a great measure of musicality to most normal living rooms (Merlins, Sonus Faber, Reference 3a's, Focal, etc.).  

What an interesting situation. But first, what is the source ?
She might prefer the sound of panel or hybrid speakers as many women do, but something is wrong with the BAT/Wilson set-up. Also, the power amp is solid state not tube, this might contribute. In addition, wall current may be bad.
A lot of work to do.

If your wife is referring to imaging keep in mind electrostatic speakers image incredibly well better than most conventional box speakers. So possibly just the difference in presentation. Though obviously also as suggested above there are ways to improve your system.

run REW

better yet, give it to her along with a USB measurement mic

repeter
Your situation is not real unusual. Musician's views of what they listen for is all over the place. They are just like us in that way. Similar musicians are closer to their shared likes.
What kind of musician is she? You do not have to answer that for us. Anyway if you are happy with your system do not worry just enjoy it.
No system sounds perfect or close to the original event. Our systems usually are comprised of the shortcomings we are willing live with for the other things they do well. It is good to find out what is important to you. Otherwise you won't be near as happy with your system for very long. If you do share the system with your wife to enjoy then maybe you can get with her to go listen to some systems to she what sounds good to her and find out why. Then make some adjustments to achieve that.