A 360 is solid state. It's only rated at 200 watts, but that's plenty. The Mesa is tubes? I don't know. If your cabinet says 371 on it, then it was part of an original stack with a 370 head. Most of 'em said 301 on them.
I have the 1968 original set up down in the music room. It doesn't get much use, since hauling it up and down the stairs is a pain, and it's a bit of overkill for the room. Usually, the Carvin sits next to it and does practice rig duties. Last week, I had a couple shows back to back and just didn't feel like setting the Carvin back up again for a rehearsal, so I ran the upright through the old 360. Lack of top end was less than ideal for upright, but holy schnitz does that thing have presence! I don't know how else to describe it. It's not loud. It's enveloping. You can hear it no matter how loud everything else gets, even without turning it up. I don't know how that works, and I'm sure it's absolutely impossible according to physics. Somehow, it sits in a mix, any mix, like nothing else. I should have plugged in a 'Bird for a while, just because. Actually, I might do that this evening, because I can. The Grexa 360 lives in a closet upstairs and comes out to play fairly regularly. N+1, y'know.