The only difference is that you have more choices of pickup combinations.
its just that you are able to have more of a curve of how sharp/creamy you want your tone to be over the sweep of your pickups
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It depends what kind of guitar you are talking about and how the pickups are wired.

The difference between 2 of three pickups depends on whether it's

H/H vs. H/S/H (like you see in a lot of modern, shred guitars)
H/H vs. H/H/H (like a les paul standard vs. 3 pickup les paul custom)
H/H vs. S/S/S (like a les paul vs. a strat)
S/S vs. S/S/S (like a telecaster vs. a strat)

the differences between 2 and 3 here all vary so you have to be more specific.