The main advantage to using pulleys is that a lot of guys already have them. I've got a bunch of pulleys sitting around, none of the double/tripples, but plenty of singles in a bunch of sizes. I don't use them for lifting, but for technical pullovers it's hard to beat the control and gearing you can get. By gearing I mean you can tune the system to get the amount of pull you need.
I'll usually start with a 3:1 using 7/8" with 9 tonne pulleys, and stack another 3:1 behind that. Stacked combinations multiply each other, with a bit of loss, so that gets you somewhere around 8:1. I can then stack another 3:1 behind that, and another 31 behind that if needed, using progressively smaller ropes/pulleys. The ropes at the tail end see less weight that the ropes at the business end. It's pretty easy to achieve 50:1, so one Groundie can pull over a substantial tree. It gives a lot more control than, say, a rope tied to a truck. Like comparing a scalpel to a sledgehammer. It is slow, and you may have to reset the final 3:1 multiple times to achieve the desired pull at the business end. I usually put some progress capture in there too.
Variations on this theme can be useful if you need to climb a partially failed tree to climb it. 2-3 guys ropes can stabilise most trees enough to make them safe to climb.