Per Yamaha's specs, the difference in weight is 2.0 lbs. MS9214 - 16.6 lbs. MS9213 - 14.6 lbs.
Honestly, unless you are only using them for indoor drumline or for middle school, go with the 14". The weight difference does not equal out to the difference in sound. The 14" snares are what everyone typically thinks of when picturing the sound of marching snare drum.
I imagine there is a weight difference, but it probably isn't much. The 14" snare drum is about the only thing "standard" in percussion, go with that. Easier to find heads, cases, covers, wraps, etc. I MAYBE would consider the 13" for a junior high group, but that's a big maybe.