I do a combination; I have a couple of power conditioners, each with 11 devices or subsidiary power strips plugged into them; these get powered on first, independently. Any gear plugged into them (including power amp, which has its own time-delay power-on to avoid pops to the speakers) comes online, and any gear plugged into the power strips plugged into the conditioners comes online as well. Next are computer monitors, then a separate power strip for control-room monitor matrix and active monitors. Last is the computer itself. Power-down is the exact reverse order.
This makes sure, as mentioned elsewhere in this thread, that everything gets powered on consistently, and that everything the computer expects to see is already there when it boots up. For a while I actually powered everything up and down individually in an attempt to be conscientious; but with so many synths, MIDI interfaces and other peripherals in the rack and elsewhere it was too easy to inadvertently leave something switched off, requiring a reboot.
EDIT:
I should also note that I have seen similar practices in "medium-large" but quite serious professional studios, like the personal studios of major artists (but run by experienced engineers and technicians); in the "big studios" (like Hit Factory in New York, when it existed, and other studios of that size and caliber) nothing ever powers down completely anyhow, except the room lighting.