The level of cooperation between Mojang and the mod makers in the very oldest days is very handwavey and before my time.
If both sides cooperate there is no real difference. If the devs don't cooperate with the modders then its a little harder with C than java.
One obvious issue relates to shipping a thousand jar files and a modder simply overwrites one. You don't need gcc's linker like you would with C.
Another interesting issue is I think the same jar file ships for all OS. If mojang shipped compiled binaries for each OS, you'd end up in situations where its hard to reach critical mass for mods. So maybe industrialcraft would only exist for mac, railcraft for PC, and buildcraft for linux, which would be too bad as they interoperate reasonably well as univeral jar files on all OS.
There is an area of architectural interest for a HN startup or whatever. Its true that GCC was a big deal to install back when I set up SLS linux off 3.5 inch floppy drives in '93 and the "C" set of SLS floppy disks was a considerable stack of disks and time, perhaps half a box of disks (five or so?). In 2014 a game installing its own captive copy of GCC (or whatever) would cost only a couple more seconds of download time. In 1980 "startup time" on an atari 2600 conditioned users to expect 2 to 3 second boot and startup times for a game, but in 2014 we've gradually trained users to expect perhaps 10 to 15 minutes total for OS boot, navigate past console ads, load a game, advertisement/commercials for dev houses, cutscenes, so don't tell me that in 2014 users wouldn't tolerate running a C linker for 30 seconds as the first step of running a game. Link while all the advertisements run, or something like that, and no one would even notice. It would make modding somewhat easier and patches somewhat smaller. I'm not talking about inventing the idea of shipping libraries, I'm talking about compiling them at part of starting the game (or whatever) up. Its an idea worthy of consideration that scales a lot better in 2014 than any time in the past.