Parasound A21 or Bryston 4BSST2?

Both will control bass very well, but which would be sweeter (more tube like) in the mids and highs?
I don't know what the rest of system consist of, anything about your room, how loud you like to listen, or your preferences. I had a Parasound A21, listened to a Bryston 4BSST2 in my own system. I don't think either one of the amps are tube like. The A21 and 4BSST are different from each other, no right or wrong...only your ear can decide what's best for you.
Perhaps you can tell me what speakers you were using, and what were the differences that you heard.

In my case the amp will be used with factory upgraded Von Schweikert VR-4JRs. The midrange and tweeters are the same as on the upgraded VR-4SRs.

Mostly listen to classical vinyl through a tube phono pre.
I have Aerial 7Ts. The A21 has a darker and recessed sound compared to the 4BSST2. The bass on the 4BSST2 is tighter and to my ears sounds bigger.
I was in your situation about a year or so ago(you can look-up my previous threads). I had an A21 for the second time and wanted to go to the next level. The logical step to me was Bryston. To my ears the 4BSST2 was different, but not musically engaging. My searched continued until I came across a Jeff Rowland Continuum S2 Integrated amp. Different price category, but I submit the S2 does have "tube like" qualities. Of course this is my opinion and if I were you, I would listen to a few amps to get a feel of the differences...Ayre, ModWright, Pass Labs, and several others out there.
I think if you want the kind of sound typical of a tube amp, you should buy a tube amp.
Sounds like you should consider some Class A solid state amps. Pass, Plinius, Clayton, etc. Best of luck.
The Sim amp I was using was neutral enough and smooth enough to let all the goodness of a tubed phono preamp (Fosgate) through. So I don't require a pure Class A. Unfortunately that amp is not usable with a heavily damped woofer system. Hence, my search. Just trying to narrow down the candidates.
Both of them are good, solid amps. I'd go with the Bryston just for the simple fact that it's relatively hand made in North America (Canada.) The Parasound is semi mass produced in Taiwan. Also, that Bryston warranty is tough to beat. In addition, the Bryston is better built. However, if you like the sound of the A21 more, then by all means, go for that.