Cold water lobsters are the Maine Type... Large claws, sweeter and more tender meat...
Warm Water lobsters are Spiney Lobsters, no claws to speak of, less sweet, and IMO a lot tougher, unless cooked correctlty...
they are more on the savory side...
The warm water lobsters are more suited to grilling than their Maine cousins...
I'm not a big fan of warm water lobsters, because of the general toughness and less sweet flavor, but many people love tham...
Warm water lobsters do make a great Lobster Thermador though, if prepared correctly and not over cooked, which seems to be the bigest problem...
Most places (IMO) on SXM overcook them...