If we use the Euler representation of quaternions does Unity avoid the problem of gimble lock that one usually gets with Euler angles?
If not, then using quaternions is easy enough once you get used to them. However, you do have to do some math to convert our intuition for angles into the components of a quaternion as well as dealing with that fact that the order you apply a quaternion matters (they are non-commutative, i.e. ab != ba). Personally, I find it easier to think of rotations as in a plane when dealing with these guys (for example, rotation around the x-axis would be in the yz-plane).
FYI, for those who want to know more here is a good technical summary of quaternions used for rotations (what is called a rotor):