Players, npc's, and objects in my game will all move from square to square, rather than from point to point. The size of each grid will be about the width of a normal character. Now, this is not going to be like chess where things hop around from square to square, though. Movement will be smooth as in any other game. The only difference between this and, say warcraft, will be that the character will always come to a stop on a grid square, and never between grid squares. This will reduce the amount of information that I needs to be transferred between client and server, and it will simplify sanity checking server-side. Also, since each grid square consists of only 2 polygons, I don't see there being a huge precision difference between the two methods, anyway.
--EDIT--
Oh, and I forgot to mention the main reason I came up with this idea in the first place: To simplify path-finding! I've already written an algorithm for some of my 2D games, which will translate over to this game with zero changes.