If warmth is the only consideration, then mittens would be the obvious choice. Mittens keep all of your fingers together instead of separating them with material like gloves do. This helps to foster more body heat and keep your fingers warmer. Warmth is the place snowboard mittens really excel. Mittens also have a small waterproofing advantage in that they use less seams so there's less of a chance for seepage. With modern waterproofing and technology, this won't make a big difference, but it's worth thinking about.
You'll likely find you need your fingers even though snowboarding is largely about your legs and feet. Doing the most simple activities with mittens can be challenging because you turned four fingers into a big, awkward mitt. Because you'll be tying your boots, tightening your bindings, turning on your MP3 player and adjusting your jacket, you'll probably want the use of your fingers. Otherwise, you'll likely be taking your mittens on and off all day, and that will cut down on the warmth factor. But if you usually take off your gloves to do any of those tasks, it won't matter that much.
Although mittens offer the best warmth, the design and technology of modern gloves have done a lot to cut the gap. Because mittens are not as convenient as gloves in any other regard, gloves remain far more popular and, for this reason, there is a far greater selection of gloves on the market.
It really comes down to the individual's preference; there's no right or wrong answer. Mittens are most useful if you'll be riding in very cold temperatures where every bit of warmth counts. Mittens also work well for backcountry riding, where you need a lot of warmth but are spending half a day hiking without the constant need of your fingers. You might only need to strap into your board once or twice so you won't lose much by wearing mittens. For most riders, gloves will provide ample warmth and be far more convenient when you're strapping in and out of your bindings. If you can't figure it out, go to the store and try on gloves and mittens and try doing things such as tightening a binding or tying your shoes. If you don't notice much of a difference and you want the added warmth, go with mittens. But if gloves are easier to use, and that's a factor, buy them. Whether you choose gloves or mittens, be sure to get a pair with plenty of insulation and a solid, waterproof shell, ideally Gore-Tex. The quality is more important than the type.