In bullet, fight till the death and then fight a little more
Is it better to allow checkmate or resign?

game is finished when i say so, not when some "global chessiverse" rules about giving up dictate to me.
never resign!
it's the matter of honor.
show them what ur made of even when they think they put u at ur knees, show them u won't kneel. they bite hard - give ur best to bite them harder!
and if they finish u at least die fighting.
you should checkmate them because they will only be too happy to let you lose on time.