Laird is for bigger guys or touring with lots of kit or if you want lots of stability. Dominator is the classic user-friendly flat water raceboard, a tried and trusted design over many years.
The Dominator is still pretty good in choppy ocean, but it is aimed at flat water. It's downwind abilities are mercurial - in some smaller conditions it is great, in some others it doesn't work well at all. The board surfs quite well for a displacement hull board though.
So, it's a pretty good all-rounder, but not meant for big choppy open ocean conditions or serious downwinding. But if you live in a place where the wind rarely gets above 15 knots it will probably be fine in just about anything you'll paddle in. The pro-elite construction isn't particularly light though, so check the price of the board carefully with the weights of other comparably-priced boards, if weight is a deal-breaker for you.
After several years of owning a Dominator I sold it to a friend of mine who had a narrower Starboard. He found himself faster on the more stable Dominator, and actually went on to become national champion in his age group on it. It's a board that has been around for so long that it kinda gets taken for granted these days. But it's a very good design that easily still holds it's own against the very latest designs -and in fact is a whole lot better than most of them IMO. Joe Bark really nailed it first time with both the Competitor 12-6 and then the Dom. Nearly all his subsequent race boards (bar the new Bark Vapor ocean board) were variations on that theme. The Laird was the variation for big powerful Laird Hamilton-sized guys, or long distance inter-Island-type jaunts.