most of these have been mentioned above but to reiterate:
Nitrox is higher O2 content, implies lower Nitrogen content, implies less narc'd at a particular depth
Less Nitrogen in the mix implies less Nitrogen to absorb into your body means you can stay down lfor longer and have absorbed the same amount of Nitrogen. Also you off-gas Nitrogen faster when deco'ing on Nitrox.
This is debatable but improved gas consumption. This seems to have more to do with not being as narc'd and hence more relaxed when diving on Nitrox than a feature of the higher O2 content. Different folks say different things about if this is true or why but it often a claim.
You are less tired after diving Nitrox. Which is GREAT as you don't have to crash out on the couch for the evening after two dives
As reagrds special equipment? Most modern decent regs will handle anything up to Nitrox 40 (40% O2). Depending on the fill system used to fill your bottles they MAY need to be O2 cleaned, then again they may not. Its not that dear to get done so it may be worth getting it done anyway. Other than that your standard gear will do you. A nitrox computer would be nice but you can use a table if you need to.
there is a lot of rubbish attached to Nitrox, if you or anyone is serious about using Nitrox i'd think about reading the Oxygen hackers companion
http://www.airspeedpress.com/newoxyhacker.html
It deals with what O2 clean actually means and why its necessary, why its not etc. EXCELLENT book