Small stages, where mic'ing anything isn't needed - Axe > Amp > cab.
Bigger stages, where the gear is mic'ed, but the audience still clearly hears the on stage sound, Axe > Mixer (Soundguy) and Axe > Amp > cab for stage feel.
If a stage relies only on mic'ed sound (Some bigger clubs or huge stages in festivals) - Just axe.
Only recently I've started to do mono, because I figured out that it makes more sense. Both, from the technical view point (Less cables and processing power, more free channels to do other stuff) and this: Most stages run mono, and if it's a big place with many speakers everywhere, splitting to L/R makes no sense.
Also, I use a personal mixer on stage, and IEM, because of a click track. (Often, I take one headphone out to hear my cab. I like my cab).