I really don't agree with him being one dimensional. Comparing Little Miss Sunshine to Anchorman or The 40 yo virgin to the Office at least leads me to believe that.
As for being script dependant, I guess that's true for some part. But that's true for every single actor. It's probably a bit more obvious when it comes to comedians though.
The movies are different, the character and manner of performance is quite similar, Little miss Sunshine being and indie film would have more depth to character of course and 40 year old virign was an Apatow film written by both carrell and apatow and it shows. The shit him an Bj Novak write for the office is terrible in comparison.
It's not that his characters are one-dimensional independent of script, just that his comedy on it's own merits is one-dimensional and unfunny which is what he reverts to with a poor script and poor direction like Date Night, which was from the same man that directed Just Married and Cheaper by the Dozen.
In one sentence: Carrell can't carry a film like other comedians can, that is why I find him unfunny in isolation.