What are the Pros/Cons of a 2.1 vs 2.3 wide Mountain Bike Tire
From Tom J. Stokes excellent article on choosing tires:

Wider tires tend to grip better during cornering and over rough terrain, at the expense of increased rolling resistance and weight. Wider tires will also float better in sandy conditions and are much more resistant to pinch flats when riding over sharp rocks or off of drops. For moderately rocky cross-country use, the sweet spot is between 2.0″ and 2.3″. If you primarily ride smooth hardpack or travel at a leisurely pace, choose a 2.0″ or even a 1.8″ tire. Likewise, if you tend to corner hard on the downhill and ride rough terrain, lean toward a 2.3″ tire. For downhill mountain biking where pedaling efficiency is less of an issue, look for a tire between 2.3″ and 2.6″. Tires up to 3.0″ wide are available, but rolling resistance becomes very significant past 2.6″.
The front tire is typically subjected to more cornering forces than the rear tire. Likewise, the rear tire is usually loaded with more weight while pedaling. Consider using a wider tire in the front with a slightly narrower tire in the back to get the cornering benefits of a wider tire with the rolling resistance advantages of a narrower tire in the rear. I’ve had good luck with a 2.5″ tire up front with a 2.3″ tire in the rear on my downhill bike.
Also note that widths are approximate. I’ve got a 2.3″ tire which measures 2.5″ wide with my calipers, and a 2.4″ tire which is actually only 2.25″ wide. Make sure that your frame and fork have enough clearance to support the width of the tire. Maximum tire sizes are listed in the owner’s manual. If you ride through mud often, allow for even more tire clearance to keep mud from building up between the tire and frame.

Honestly though, the difference between a 2.1 and 2.3 is very small - I would just get the highest quality tire you can afford that is between those measurements.