I looked at both and decided on the Boss for two main reasons. For one thing it has LOADS more memory, which is important to me since I don't do MIDI, at least not yet. All my songs/patterns are unfortunately stored on the unit itself. I also liked the sound of the instruments better on the Boss.
This is a lesser factor, but I also liked all the editing that was available for individual instruments on the Boss. However, now that I've built a small set of kits that I use for almost all of my programming I don't do much tweaking anymore. But it did let me get the sound I wanted.
I don't rememebr off the top of my head if either had a much larger number of instruments to pick from but the Boss gives you 255. Well, 254 if you don't count "nothing" as an instruement. Yep, that's right, you can have complete silence be one of your percussion instruments. There actually is a reason for this though. I once decided that I didn't want to keep the cowbell I put into a song, so I was able to quickly "remove" it by changing the instrument for that pad from "cobwell" to "nothing".
Of course, the flip side is that the Boss is now almost double the price of the Alesis. Also, since I don't do MIDI I can't comment on how easy it is with the Boss. I've read that the Alesis does it well.