From what little I understand SOP (Seat Of Pants, for Mary):

Think about hull shapes.
An assymmetric cat doesn't work unless it 'bites' the water. Even on a heel, you've got quite a bit of 'v' hanging below. If you didn't, the boat would merely be pushed off sideways, with nothing to stop it, well, except the rudders. Thass displacement if ever it was.

Other designs involve fine bows with hemicircular sterns. Now in the case of these boats, it's a matter of the WWW factors and speed. At lower boatspeed, windspeed, rougher water (either/or) you're gonna want to sail the boat bows down, or in displacement mode, which as it turns out is most of the time. But if it's flat, or blowing stink, or you're really 'sheeting in and maxing out', you'll set the boat more towards its sterns and begin to plane to some degree.

Looking at the newer designs, the Inters in particular, are designed more as a planing boat, with rather flat bottoms. But regardless, when you're going slow, cats are displacement, and depending on the hull design, as you go faster, they begin to plane.

So the answer, to me, is...
BOTH.
Depends on the hull design and WWW factors.

sea ya
tami