I recorded with a flat EQ directly onto a digital medium using jacks and it's a good recording. I might add a bit EQ in the final mix though but it depends on what the other instruments do. Signal levels were a bit low, ballanced output should boost it though, improving S/N ratio considerably and allowing you to do more in the mixdown.
As for stage I can't really say, amplification feedback is a factor which may need changing the initial EQ but on stage it also depends on how well you like the monitored sound, after all the better you like that the better you usually perform.
Ludwig