The simplistic way that I understand it is the larger pick up samples ("hears") more of the string (thicker sound) and the smaller pick up samples less (thinner sound).
That having been said, I can obtain a thin bright sound on my Skylark, which has the larger pick ups, by manipulating the tone and volume controls and the Q switches.
In fact, the only sound I can't accurately mimic on that guitar is the out of phase "quack" sounds produced by a single-coil equipped Strat-style guitar when using the 2 and 4 positions on a 5-way switch - but I can get pretty close.