That Wikipedia article is biased. From
as of Apr 18, 2014:
When composing several rotations on a computer, rounding errors necessarily accumulate. A quaternion that’s slightly off still represents a rotation after being normalised: a matrix that’s slightly off may not be orthogonal anymore and is harder to convert back to a proper orthogonal matrix.
This is biased. There is nothing hard about re-orthogonalizing a rotation matrix, see for example:
and Quaternions have to be re-normalized too: "A quaternion that’s slightly off still represents a rotation after being normalised". Quaternions don't have a significant advantage here.
I will try to fix that in Wikipedia. This biased opinion shows up in Wikipedia at other places as well... :(
That answers your question.
UPDATE: I have forgotten to mention: gimbal lock doesn't play a role here; neither quaternions, nor rotation matrices suffer from this.
Some side notes. Even though quaternions are more compact than rotation matrices, it is not at all a clear cut that using quaternions will result in less numerical computation in your application as a whole, see:
Just for the record: rotation matrices have been used with great success on resource constrained micro-controllers to track orientation, see Direction Cosine Matrix IMU: Theory by William Premerlani and Paul Bizard. I also have first-hand experience in tracking orientation on a micro-controller (MSP430) and I can only second that rotation matrices are fast and stable for tracking orientation.
My point is: there is no significant difference between rotation matrices and quaternions when used to track orientation.
If you already have a library that uses quaternions to represent rotations then stick with quaternions; if your library already uses rotation matrices, then use rotation matrices. Even if one representation would save you some floating-point operation here and there, there is no point in changing your application / library to use the other representation; even on resource-constrained micro-controllers, the savings would be insignificant.
The only true advantage of quaternions that I see is that quaternions can be used for interpolation. Neither rotation matrices, nor Euler angles can do that.