I am a very big fan of pressurized fermentation. The benefits I see, in rough order of the value I place on them:
1) Pressurized ferments streamline my process tremendously.
This is the big one. Once my wort is chilled, I transfer to a regular corny keg (just under 5 gallons). I keep the fermentation at 5 psi until it starts slowing down, and then I cap to my target carbonation level. For most beers, that's it. I cold crash, hook up to gas, and serve directly from the fermentor. That means less equipment to clean and less equipment to manage.
2) Oxygenation is simple and consistent.
To oxygenate my wort, I simply fill to the fill line and then bubble canned oxygen through the liquid diptube until I hit 4psi. With a liter and a half of headspace, by my math that puts me right at 15 ppm O2.
3) The pressure keeps blow-off down
I like fermenting in corny kegs because they are they cheapest stainless steel vessel I can find. However, they're a bit small. WIth a bit of pressure and a bit of fermcap, I'm able to ferment with them nearly full with only a very small amount of blow-off.
4) I use less CO2.
This likely isn't a big deal for most people, but where I live getting CO2 is a major pain. Since I started pressure fermenting, my CO2 cylinders have been lasting 3 times as long. That's two fewer trips to the welding store for every trip I still have to make.
5) I can ferment warmer and thus don't need to cool as much.
Because pressure inhibits ester and fusel formation, I ferment a few degrees warmer than I otherwise would to achieve similar results. I use thermoelectric cooling for space reasons, which is relatively energy intensive. This means I don't need to use as much.
For what it's worth, I'll thinking of switching to a pressure-capable conical at some point in the near future. This would change my process somewhat.
(I'll keep this list updated if I think of anything else.)