Alright, It depends on various things, most of which you haven’t told us, several of which you probably don’t know. In all likelihood, the shorter end will be more massive, because distribution of mass around an object’s center of mass is weighted by distance from the center of mass (less mass counts for more, the farther out you get). Again, in general, if an object stretches out further in any one direction from it’s center of mass, or has more volume in one direction from it’s center of mass, the opposite direction will have more mass closer, or in less volume, to compensate (in order to keep the center of mass where it is). In an object of constant density, the center of mass will be the same as the geometric center, but only if the object is split in half along a plane of symmetry will both halves have the same mass. On top of that, if an object varies in density, there’s no guarantee that even that will be the case. If your broom had a lead weight in the stick, placed in the right location, and was then cut in two, through it’s center of mass in the way we’ll assume is obvious, both sides could have the same mass. For a short, simple answer that’ll do in most cases: see ben.
It should be noted that when considering things in physics, short, simple answers that’ll do most of the time, but we know don’t work all the time aren’t good enough answers.