Here is a link or two I found when looking for the benefits.
The best quote from this site,
straightdope.com, is this one.
Oh, there are plenty of benefits: (1) Cool fluorescent green valve stem caps (assuming your nitrogen vendor has any marketing savvy), which will look sharp with your spinning wheel covers. (2) Bragging rights. OK, you were behind the curve with cell phones, iPods, thong underwear, etc. Nitrogen in tires is relatively new to the mass market. Now's your chance. (3) Reduced fire danger next time you land your space shuttle or commercial aircraft, and tell me you won't sleep better knowing that.
(More for those that don't want to go to the link)
As for moisture, changes in humidity affect tire performance two ways. First, the density of humid air fluctuates more with temperature than that of dry air, so removing humidity can keep your tire pressure more consistent, especially when the temperature climbs over 100 degrees Fahrenheit. That may be a legitimate concern in Formula One racing, but it's not much of an issue if you're just tooling around town.
Humidity can also be a factor in wheel maintenance - since pure nitrogen doesn't have moisture in it, supposedly your wheels won't rust as quickly, which could lead to improved wheel performance and air sealing. The question is, how big a problem is wheel rust these days? According to a few tire and wheel shops we contacted, not very. Seriously rusted wheels are uncommon in typical steel-wheeled cars, and many high-performance cars have alloy wheels that don't rust at all. One exception is work vehicles such as dump trucks, which are exposed to a much harsher environment.
Another claim I've seen is that since nitrogen is slightly lighter than air, you'll save weight and get better performance. However, we're talking about a weight difference of less than 4 percent of the gas in the tire - in other words, a difference of less than an ounce for most vehicles. A possibly more realistic benefit is that nitrogen is largely inert chemically at low (i.e., normal) temperatures, so it won't attack the rubber in your tires like oxygen does. Oxygen attack is something both the National Highway Traffic Safety Administration and Ford Research have studied, and can be a problem for tires used for a long time or in rough conditions.
Now here is a couple of links from the Getnitrogen.org web site.
Science
Why
To me, unless you can get it for free, it just doesn't seem worth spending the money on. Sure at some filling stations you have to pay to use their air pumps, so why go with nitrogen if it is going to keep you away from the pay pumps. I guess that is logic some can live with, but I've never had to add air to my tires (second set) and if I did, the gas station near me has it for free.
So if you want to go with it because you 1) feel better about using it, 2) have concerns with wheel rust out, or 3) don't mind a minimal cost, then happy driving. I add this bit, $150 is not minimal when you consider the tread life on the tires we use on this car. To me that money is better saved towards replacement tires.