How does my MF A308 compare to modern integrated amps in the $3000-$6000 range?

I'm with @jjss49 

Mostly what you'll find out there will only be different, not unequivocally better or worse.  Unless there's a particular aspect of your sound that's lacking and needs addressed (and is easily attributable to amplification), I wouldn't start a new search. 

If you do start wandering, I'd try to start sampling totally different typologies (e.g., a full tube integrated, a class d integrated, an otl) rather than just sticking with other class a/b amps. You'll learn more that way.

And as always, amp to speaker matching is an essential and hard to fully predict challenge.