Musician vs. audiophile

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. 

You did not state what power amp? Assuming it is a BAT too but who knows.
Now I must state from personal experience and a number of other comments I have read that BAT and Wilson speakers are usually a marriage made in heaven IF everything else is correct. I have no experience of the BAT preamp but I use a BAT power amp to drive my Wilson's and I am wanting for nothing. Imaging and soundstage are superlative and bass response can cause bowel movements....lol.
Even at low levels for evening duty I am losing nothing and flat is not a word I could ever use.
Als suggestion to disconnect the subs is excellent and the first place to start. 
You also have no mention of source? Streaming, CD,vinyl?? Could be numerous issues there too.