I have both of these sizes in the same shell, from the same company.
Deathmetalconga was pretty on, but I'd like to add that, it's easier to get the clearer tone and you can also hear each stroke a bit clearer when doing multiple strokes.
The 12 deep can have "more resonance" but, if you are loose with the tuning, the 12x14 can sound a bit hollow if you aren't careful.
More resonance can be good if the drums got a full tone and a smooth decay evenly and isn't just "ringing" longer.
To my ear, the 11x14 sounds like a big tom, and the 12x14 is more like a small floor tom--which it's great for, as it can be quicker and fatter sounding than a 14x14 (I have 12x14 and 14x14 floor toms too).
If you are looking for a big sound, but need a clean sound out of the big note/tone, then a 10x14 might be better if it's available from the company you like--otherwise, for a tom I'd suggest the 11x14 size as opposed to the 12x14.
One more thing...you can play the shorter depth toms dynamically easier and with less loss of good solid tone than a deeper one.
It might not matter if you are playing hard most of the time--the 10 or 11 deep can "take it" as well as a 12--but if you want to play the drum lighter sometimes, or in certain passages of songs, you'll get better overall results from the shallower drum.
Hope this helps.