It is normally a very tough situation for some contestants to decide whether they want to take the November HMMT test or the February HMMT test. As the HMMT rules state, "due to spacing limitations, no student can attend both the November and February competitions." This page details the main differences, besides the obvious.
Before the November HMMT was introduced, the Harvard-MIT Mathematics Tournament was held at Harvard University for even years and the Massachusetts Institute of Technology for odd years. When the November HMMT was introduced, the rules changed, and now Harvard University is the location for all November HMMTs, and the Massachusetts Institute of Technology is the location for all February HMMTs. However, Friday-night events are at the opposite school (for both competitions).
For the November HMMT, the team size ranged from 4-6 students. For the February HMMT, the team size ranged from 6-8 students. No organization is allowed to send more than five teams for the November competition, and three teams for the February competition.
The November HMMT has a difficulty of about mid-AMC to upper-AIME. The February HMMT has a difficulty of about upper-AIME to olympiad. To get a feel as to what those problems look like, visiting the HMMT Problems and Solutions page and looking at a few problems might be useful.
While the November HMMT has a team round that is short answer (like all of the Individual Tests), the February HMMT has a team round that is proof-based. This is meant so that more-experienced high school students can get exposed to what proof-based mathematics is all about.