|In general I think belaying off the anchor is a better option. However there are a number of scenarios where I prefer to belay off the harness, these include: if the anchor is by necessity in an annoying location, too low, off to side, perhaps if the device would unavoidably get pulled into an annoying crack (can't think of a time that's been an issue); if the anchor is kinda shit and my stance is part of the belay; if the second is moving fast on easy ground; or if the particularly combination of autoblock device, rope and belay biner creates a metric ass ton of friction. In general only the last two scenarios might have me contemplate a redirected belay, which I only do very infrequently.
As is often the case in climbing it's best to be competent and comfortable with a range of solutions and approach each situation with an adaptable mindset.
Edit to add: I think too much is made of the safety arguments for using an autoblock - that it will continue to function with a belayer of unreliable consciousness (for whatever reason), ease of escaping the belay, etc. The immediate value lies in letting the belayer direct their attention to other tasks like eating, drinking, sorting the rack, or butt scratching without it being any less safe for the second; additionally if the second is going to fall a lot and hang around on the rope, it's generally a drag to have to hold that weight from your harness.