Lately I've been experimenting with a mix of traditional kettlebell exercises (swings, snatches) and bodybuilding exercises (military presses, curls, etc.) and I think that overall it's easier to injure yourself with traditional bodybuilding type exercises.
With many kettlebell exercises, you are not isolating parts of the body the way you do with bodybuilding workouts. A swing or snatch is pretty much a full body exercise, distributing the load over a wide range and from your feet all the way to your hands. Of course some parts of the body are stressed more than others… when doing kettlebell swings you'll feel it the next day in your inner thighs (which is probably NOT where you expected to feel it!), but distributing the load makes it less likely that you'll hurt a specific muscle or tendon IMO.
The whole concept behind bodybuilding is isolation, the goal being to work individual muscle groups separately and intensely. I believe that this is more likely to lead to injury, especially when combined with the standard tactic of doing reps to failure.
I found myself getting twinges and having to back off when doing various bodybuilding moves when I didn't feel this type of thing at all with kettlbell exercises.
Now this is not to say that you can't hurt yourself with a kettlebell, so please do be careful. A friend of mine actually broke his finger when he lost control of it, it bounced of the coach and landed on his hand (OUCH!). But if you're careful and know your limits, I think you'll avoid injury and build better overall strength using kettlebells.