To expand a bit, I wish it was included in the comparison not only because it has some big advantages, but also because it has some drawbacks worth examining.
The top-level zones are its weakness. The further apart two coordinates are from each other, the more difficult it is to reason about their relationship. MGRS works fantastic for reasoning about coordinates on the same grid square, but gets harder as you move up to comparing between grid squares and harder still as you compare between zones.
A grid square is 100km x 100km, so it's pretty big, and coordinates in the square are easy to manipulate. If you know your office is at 4QFJ 21631 04440 and the Starbucks is about 500 meters down the road to the north, then you know Starbucks' coordinates are roughly 4QFJ 21631 04940. To indicate your uncertainty, you'd say 4QFJ 216 049, or possibly just 216 049 if the grid square was already known from context.
The system is typically extended to allow that reasoning to work even at the edges of a grid square, by allowing eastings and northings that extend past the grid square edge. This means there's more than one possible way to describe a location, though only one canonical way. Unless you're already familiar with the area, you may need a map to compare coordinates on different squares.
Some of the grid zones are also a little oddly shaped. It's mostly not a big deal because they're huge, and it really only affects which coordinate representation is the canonical one at the boundaries, but it would be nice if the top-level 6° by 8° grid zones were more regular.