As Harvey mentions, it's a pretty common misconception that LDC's have more bass response than their smaller-diaphragm counterparts.
There might be a small sliver of truth to the theory, though, only from another perspective: For example, most LDC's tend to be designed for vocal work, and are usually intended to color the sound/voice in certain flattering ways, which often means extra peaks and valleys in the freq. response. Indirectly, this often results in what we perceive to be a "bigger" sound due to the built-in smiley-face curve.
Another common theme you'll find is that a lot of larger diaphragm condensers tend to be more directional. Again, you can't make the general statement that LDC's are more directional. But you probably could make a case that more of them are just designed that way for whatever reason. And greater directionality does most often mean more proximity effect, and hence a heftier, bassier sound.
Again, though . . . just because a lot of LDC's tend to sound a certain way, and SDC's yet another way . . . doesn't mean that all of the differences are attributable to the size of the diaphragm.