I’ve run my axe FX ii though a few different poweramps.
My rectos power amp sounds cool, but it just makes everything sound like a Recto. If I want that, I just play the Recto. It was the most colored of every power amp I’ve used. I’ve read this is common with Mesa power amps, they give the ‘Mesa sound’ no matter what.
I also used a Fryette 2/50/2 for a long time, sounds very good, more on the neutral side, but still a tube power amp sound. Some amps sound good with power amp modelling on, and some don’t. It can be easy to get that overly-scooped double-power amp sound which isn’t great. More fiddly to set up and tweak than using a solidstate power amp.
What I use the most is an old Matrix M400 solidstate mosfet power amp which is flat respsonse. Easier to set up than all the rest since that’s really what the axe FX was designed for.
If you want to use the axe FX as preamp-only, then a tube power amp is a good idea, but if you plan to use the full amp models, I would go solidstate. A neutral tube amp can sound just as good but is more work and tweaking to set up, in my opinion.