As far as tube power amps, the biggest difference will most likely be in the type of power tubes being used (6L6, EL34...). Beyond that, there is probably enough "tweakability" in the Axe to make them all sound pretty close (tonewise). I've used a few, and am currently using a TS100. Which Matrix amp did you try, and what didn't you care for?
Are you using a TS100 as well? Honestly, I have no complaints with it at all.
I started with the Ultra and a Matrix GT1000. Hated it. First, I noticed, without comparison, that it was lifeless, dry, pale. I started to think about my Bose power amp that I use for my studio. Bamm. Killed the matrix. No ifs, ands or butts. Also, it is big and heavy.
So, then, I figured, because of the infinite search, that I'd try tube power with the ultra after talking to a tech a Fender.
There are many out there, and the price varies considerably depending on what you get. So, I started entry level. The Carvin for $300.
It kills. I have wood and glass coming out of my Gibson all day long. Where you get it is in the quality and depth of the mids, and lower mids.
My tone right now kills. I am just playing around now. Sure, I could go VHT, or other stuff in the thousands, but why? At this point, if I get a 20/20 and like it better, I'm good already. If I hate it,...I'm still good, with my cheapo TS100 that sounds great. The Carvin was $300, and my Matrix was $750, so money wasn't what I was hearing. With V-30's or V30/g12h mix. I would say that using an Axe-fx with ANY transistor amp, WILL NOT allow you to truly hear what the Axe is putting out. JMHO