If it's a larger venue, I use the DI and use my amp as a stage monitor. If it's a smaller venue, I use the stage volume. I find most mics aren't that good at handling bass amps. The SM57 always seems to be struggling, while a Beta-style mic loses highs. In my experience, most sound guys are better at dialing in a good tone with a DI. I always think asking a sound guy to deal with mic'ing your amp and running a DI is a little prima-donna-ish.
That said, I have a pretty rounded, vintage style tone that's easy to reproduce witha DI, and have been blessed by randomly getting good sound guys. Plus, I play all originals, so we're on for around 45 minutes to an hour most shows, meaning the extra time spent dialing me in is time cutting into our set and possibly the next band.
Of course, if you're running your own sound, or if you play covers for a three-hour gig and are familiar with the sound guy or have one that you hire, all bets are off and you can be as nuanced as you want.