I haven't played any gigs yet with my Heartbreaker, but I use Tweed all the time with 6V6, or Full all the time with EL-34's.
I would probably use Tweed for smaller gigs with EL-34's though since it is as loud as it is heavy! :lol:
When I used a Mark IV, I almost always used Full for practice or gigs and Tweed for playing at home.
The problem I have with Tweed is that I really like how punchy the amp is on Full and can't seem to get used not having that punch. I'm not an overly technical player and rely more on dynamics and choice of note.