Prefer semi=weighted and presets as opposed to lots of menu diving.
As stokley alluded to, people classify different kinds of boards as "synths." If you mean synthesizer in the classic sense, action will almost certainly be unweighted or semi-weighted (not fully weighted/hammer), and the choice would not be between presets and menu-diving, but rather menu-diving vs. direct controls. Boards with menu diving will have presets. Boards with direct control may or may not have presets.
All the other comments here are filled with good ideas/questions to try to narrow down what you're looking for.