BTW, are you asking about just the original 3560 and 3750 switch models, or the 3560 and 3750 switch families (e.g. 3750/3750G/3750E/3750v2/3750X)?
Except for data stacking (and, I recall [?], power stacking on the 3750X), more-or-less, 3560s are the same as the 3750s. Often there are almost identical "twins" between 3750 and 3560 models.
I recall there are a few models of the 3750Gs which do not have a like "twin" 3560, such as the (rarely seen) 3750G with a single built-in 10g port, or the 3750G-12S which supports additional (and larger resource) SDM templates unique to it (useful if switch used in a distribution role). I suspect there's not an exact 3750 and 3560 twin for every model and no twins at all for the 3560 compact switches, but generally they are both using, I believe, the same underlying architecture except possibly for the 3560-C and 3560-CX, which might still use original 3560/3560G architecture or might be using like gen 2960 architecture.
