The biggest difference between Frangipani and Cuisianrt (besides Cuisi's higher price) is that Frangipani is more of a boutique type hotel with less than 20 in accommodations whereas Cuisi, more of a resort hotel, has more than 75 rooms, a lobby, gift shop, and other amenities.
My only other comment to you would be to do SXM first for the fun, running, shopping, dancing, doing, dining, gambling part of your vacation and end up at AXA for mind and body enriching, a tranquil and stunning beach experience(one after the other), a plethora of food dining from upscale to casual, and locals who are so warm and friendly you'd think you'd known them all your life.
In other words, AXA's got the "soul", darlin'!