My old, shorter snowboard, or my brother's longer, wide snowboard?

do not choose the wide, it will feel like riding a door. as far as your toes hanging off a bit that is a good thing, you want your feet to hang off just a bit, but evenly... what you should do is take your boot without your foot in it and strap it into your bindings on your board. if your toes hang off more than your heel, take the boot out loosen the screws and push the bindings back a bit till you got even hang. a 10.5 could go on a mid wide board, but not a wide. you wouldnt have to much fun on that.

Between the two, the smaller board, for sure. I'm not sure if you meant your FEET or your BINDINGS extended beyond the width of the board, but regardless, both should at least a tiny bit. The bindings you pretty much want to extend perfectly from one side of the board to the other. However, since this often doesn't happen, snowboarders angle their bindings inward (for free riding/alpine racing) or 1 inward and 1 outward ("duck stance" for freestyle). Experiment with binding angles to find something comfortable. Now once you sit your feet in the bindings, there should be just a little bit of boot overhang over the side of the board, providing leverage for easy-to-make turns. Just be sure not to have too much foot overhang over the front of the board, or your feet will drag making toe-side turns. Again, angle your bindings appropriately inward or outward to solve this problem. If you can't angle the bindings enough to prevent binding overhand, then your bindings are obviously too big. If you can't angle the bindings enough that there's only a LITTLE bit of foot overhang, then the board's too narrow for your foot size (which at size 10.5 really shouldn't be an issue for a regular width board).

Go with that guy above