I just measured a couple of my "normal" ukes, both tenors. The Mainland is 2-3/4" and the Cordoba closer to 2-1/2". I don't see that 3" would really feel much different playing.
Now, in theory, a larger chamber could offer more resonance and a bigger sound. But in reality, there are a lot of other factors to consider, such as the woods involved (both top and back/sides), thickness of the wood itself, solid vs. laminate, bracing, etc.
My Kala spruce top thinline tenor (a mere 1" where the neck joins and 1-1/2" at the bottom of the lower bout) is a very loud and bright instrument, much moreso than my mahogany Cordoba.