The simplest answer is that a disc will turn the ground over and a pasture renovator will just cut slits in the ground to let air and fertilizer get to the root zone. Weight and the number of discs/teeth determine how deep each will cut. Agressiveness on a disc is determined by the angle....more angle=more agressive. The more passes you make with a disc, the more it breaks down the clods, and the closer you can get to a powder consistancy.
The size of the pasture, the number of horses on it, weather, how often it is rested, fertilized, soil tested, type of grass, etc, determine how often you should have to do anything to it. I have 14 seperate paddocks for an average 20-25 horses and I rarely strip a paddock and reseed it. If I get an area that they have compacted so bad that grass will not grow on it (fence line, water trough/feeding area), I'll usually use a tiller on it and reseed it while it's resting. I'll also fertilize it, mow it, and spray it for weeds while it's resting, depending on what it needs. I've got a soil test kit (LaMotte AST-5) so that's easy to determine.
Except for Spraying/fertilizing/cutting/raking/baling, we never go into the hay fields so I don't worry much about compaction. If I needed to run a pasture renovator over them, I'd borrow one before I'd buy one. It would rust out before I could wear it out.
If I do need to strip a paddock, I'll typically disc it to turn over the soil (a disc will cut into very compacted soil) and then run over it with a tiller to smooth it out. I spread seed with a cone spreader 10# of bermuda with 100# sand, and run over it with a chain harrow (drag) to improve the seed soil contact. Sometimes I'll run over it with a pasture roller....just depends on how I feel about it. I keep horses out until the grass is about 6-8".
When I plant rye for the winter, I just overseed it in the fall...I can do that while horses are in there.
If you manage your pasture and the grass in it, you should rarely have to do much with it. A fence to allow resting is probably your best implement. It's also the cheapest.