Buying used can result in spending significantly less money. There are some risks, of course, but if the tank is currently being run with similar inhabitants that you're interested in (i.e. -- as a reef tank and you want a reef tank; or as a FOWLR and you want a FOWLR) the risks are quite low. If you're buying a tank that has sat dry for a period of time, a little more caution should be taken. Depending on the age of the tank and how it was stored, potential problems can range from the tank no longer being water tight to contamination from household cleaners, oils, etc. As a precaution, every tank that I've purchased used that was stored prior to me buying it has been thoroughly cleaned with either vinegar or bleach, scrubbed, and heavily rinsed with water. I've bought several used tanks that were stored prior to sale and put them through this, and had no problems with any of them. I could just be lucky, but so far so good.
Buying new has the greatest advantage of being able to get exactly what you're looking for, generally without having to look too hard for it, as long as you're willing to pay for it. Tanks purchased new typically come with some sort of warranty, which you don't get when buying a used one. While I'm not sure how common this is, a couple of the LFSs around here give something like a 20% discount on all accessories (including LR) if you purchase a new tank set-up from them.