KT-77 vs. KT-66

as a generality, kt66/6l6 tubes are basically a weaker (less powerful) el34 -- they will usually sound weaker/slower in the bass, and sometimes a touch more ’beautiful’ in a classic tubey manner in the lower treble, mids and upper bass

but obviously, tube makes within a type, can have sonic differences that may overwhelm that across tube types (a gec kt77 vs a shuguang el34 may would sound more different than a modern russian sovtek kt66 for instance)

I'm not familiar with your amp.  I think your question tends to be amp specific.  In my Decware ZMA, I preferred the KT66 over the KT77.   however, steve Deckert designed the amp around the KT66.  I did a long journey of tube rolling and ended up right back where I started.  That said, my second favorite in this class was the inexpensive russian 6P3S.  Won't cost much to try it. 

And of course tube manufacturer plays a big role.

Jerry

KT66 and KT77 are both great tubes as @jjss49 states above the 66 will sound more classically tubey and a bit warmer but they sound great to my ears. Worth exploring since it's an option for you @hilde45