In our household, we have owned and dived neoprene, compressed neoprene, laminate suits and the Fusion (which is a weird one-off).
Neoprene is warm and usually cheaper, but neoprene will lose it's insulating properties over time, and the buoyancy swings are a bit more difficult. It's heavy, not as flexible as one might hope, and dries slowly.
Compressed neoprene doesn't have the issue with buoyancy and does not seem to change its insulating capacity with multiple dives over time. It's tough stuff -- my husband has yet to have ANY leaks from his four year old suit. It's significantly heavy and dries slowly. It's also hard to glue things (think pockets and p-valves) to.
Laminate material is light and dries very quickly. It is not as tough -- easy to put holes in it, and sometimes quite difficult to find them. It's easier to glue things onto, and very easy to repair if you can find the leak. Laminate does not stretch AT ALL, so buying a suit with adequate mobility for your purposes is critical. All insulation in a laminate suit comes from the undergarment, and you will need a heavier one than you will with a neoprene suit, for the same water temperature. But laminate suits are versatile, because you can dive them comfortably in a wide range of temperatures, simply by using lighter undergarments.
The Fusion is a peculiar dry suit -- a bilaminate bag with a stretchy outer covering. Because of the stretchy "skin", the bag can be cut quite large without running the risk of ballooning. This gives you the mobility of a wetsuit with the warmth of being dry. The disadvantages are the difficulty in figuring out pockets on a stretchy outer covering (there are solutions, but I'm not delighted with any of them) and figuring out footgear (but that is an issue on any suit that uses a nylon or neoprene sock instead of a boot).
Each choice has its pros and cons, and price can vary wildly (more than a factor of 2) between models and brands.