There are lots of promoted benefits of pure nitrogen. Separating the truth from the snake oil is difficult.
To be clear, what you're getting is "more nitrogen". The normal air you pump in is 78% nitrogen. What those services really offer is getting out the water vapor and oxygen.
Nitrogen passes through tires at a slightly lower rate than oxygen so your tires should stay inflated slightly longer. Of course, when they are low you'll either have to add regular air (no problem) or go back to the service station.
More importantly, you won't have any water in there so the tires will heat more evenly which *should* improve their life span.
The other benefits I'm aware of are more noticeable in race applications where getting 1% better response is the difference between 1st and 2nd place. Hopefully that doesn't apply to your daily driving.
