I've gotten more injuries in BJJ and grappling, mainly because early on I didn't know how to intuitively roll to prevent injury, and my old gym was full of gym heros who would crank, go ham on stuff they saw on youtube, and I took the brunt of it. Stuff like a single leg counter by rolling into a kimura, I didn't know what that was, I was locked, and my shoulder went. Most of the injuries there were more on the fingers and toes though. One that was funny and sad at the same time was getting knee tapped, and I fell on my side and got cut; The cage wasn't set up properly, had a loose wire sticking out, and my forearm gashed on the fall.
Almost had my neck snapped by an idiot; Guy locked me in a guillotine and decided to throw me while locked in what looked to be an attempt at a throw to land in scarf when it was to the ground. By some miracle I got free midway and fell in a scramble. That point I basically went all out after, and given he was retarded in striking, it was easy pickings.
MT, my injuries have usually been ribs from fights, or ankle swelling (dunno how these happen, I never recalled kicking a knee, elbow, or even eating a check on that area, so why it gets swelled there is still a mystery). If in training, it was because a dipshit didn't have the technique down and tried to go fast hitting an area that wasn't really supposed to be hit in the drill. eg. catch a kick -> sweep, and hitting the side of my knee at 100% because it's a drill and not sparring.
Long story short, grappling injuries are more freak injuries (incl. getting doubled, and falling into people behind us), and striking its more manageable. Also, not exactly injury like, but on a similar topic, there's more dirty people in grappling, I have no idea why. Dudes who don't cut their nails, and I get cuts off sharp toenails etc. I'm lucky to not have gotten anything really major, whereas a couple of teammates weren't. One almost got his knee blown out on a heel hook, when a sister gym's coach came with some students, my teammate got a good toe hold on him; On the next round he cranked out a heel hook on my mate because his students saw him get subbed.