Going from the Adcom GFA 555 ii to the Bryston 4b SST or SST2?

It's possible and likely you'll hear a difference, but there are too many variables involved to know exactly what improvements you'll hear.   Which you'll prefer is subjective.  What speakers are you using?

 

You will likely hear a difference, but as previously stated, it will be up to your ears which you prefer. Tell us about the rest of your system. Your preamp could be a significant factor. 

The earlier Bryston's (NRB, SST) are a bit dry sounding, maybe a bit shrill. the later ones are far better. SST2 and up for sure if Bryston is your thing. 

Both will be an improver. But the SST2 will be the more satisfying improvement. The SST will have a bit more slam. But put your money into 2 steps up rather than one. The SST2 is highly regarded.