Does garbage disposal horse power matter that much? I am in the last leg of a kitchen remodel and need to purchase a garbage disposal. And I am wondering how much of a difference horse power makes in the day to day operation of the kitchen?

Has anyone here experienced the pros and cons to disposal units with different horse power?

NOTE: I almost posted this question on the DIY site, but I feel it has more relevance here. Moderators, feel free to move it if you think it belongs there instead.

UPDATE: We decided to go with the Waste King L-8000 Legend Series 1 Horsepower. It is really smooth and quiet. It takes up a fair amount of space under the sink however.
I'd go for a more powerful one, in general, and I noticed that the higher powered disposals are sometimes quieter, which I really like.  I really learned that paying the extra for good plumbing parts (faucet, disposal) through our plumber was worth it, since they can be fixed, unlike cheaper big box store stuff, and that there was a real difference in the higher quality disposal.