Earlier quoted context omitted.
I couldn't tell you without a specific example, but I would suspect distributing an edited ROM would be much easier than save state hacking. In a general sense, I suspect the latter is more popular because it's not illegal to modify/distribute save state data; ROMs certainly can be.
They distribute delta binary patches on the form of IPS formats.
Obviously, if you want all 151 Pokemon captured, you would do that through a save state. But if you want increased chances of capturing Pidgey, it would certainly be easier to distribute a ROM (or delte, in this case) with those new ratios baked in.