Residential waste disposers are generally available with 1/3 to 1 horsepower motors, with commercial units having even more power.  Really, it's hard to imagine any of these power options being a problem; 1/3 horsepower is plenty for chomping up everyday food scraps, and if you need more power than that you might want to rethink what kinds of junk you're shoving down the hole.

There are, in fact, two general types of disposer: continuous feed models, and batch feed models.  Most models you're likely to find are continuous feed models; the idea here is that you run the water and start the disposer running before you put any scraps in the hole.  In other words, the unit is not designed to have to start from stationary with scraps in the disposer.  Do you feed the scraps in while it's running?  Not likely; most people put it in the hole first, then hit the switch -- and this is how disposers get jammed.  Fortunately, disposers include a breaker that will trip if the motor gets jammed, and some include a wrench that you can stick in the bottom to manually turn the rotor.  Some of the upper-end models even include an auto-reverse feature to clear jams.

The batch feed models are intended to be loaded before starting.  You can tell these models by the way they are operated; the plug must be inserted into the drain and twisted to start the disposer.  Perhaps a good safety feature; you theoretically cannot have your hand in the disposer when it's running.

Regardless of the type disposer, you probably don't care about the power as much as you care about the starting torque or stall torque.  Unfortunately, nobody advertises their stall torque.  Even if they did, you'd have to check the diameter of the turntable to be sure you're comparing apples to apples; a larger turntable requires more torque to provide the same force at the edge where the shredder ring is.

Now, to throw a really big monkey wrench in the discussion: there are two general types of motor used in waste disposers.  Most have split phase induction motors, and you can tell these by the rpm written on the box: 1725.  However, there are also disposers with commutator motors, and these generally spin much faster; the ones made by GE are rated at 8000 rpm.  Commutator motors are considerably smaller than induction motors, although that might not be apparent underneath the sound shielding surrounding the unit.

There are more differences, though.  When a motor turns faster, it doesn't require as much torque to develop the same horsepower, so a motor that turns 8000 rpm can have less than 1/4 the torque of the induction motor with the same horsepower rating.  That's not a problem, though, for two reasons.  First, since the commutator motor turns faster, it can be made with a considerably smaller turntable and still move the scraps through the shredder ring in a hurry, and a smaller turntable means less torque needed.  Second, commutator motors inherently have a lot more starting torque than induction motors -- and, as mentioned above, starting torque is where it's at with waste disposers.  The long and short of it: either type motor seems to work pretty well at disposing of waste.

Commutator motors -- especially ones with permanent magnets -- are also considerably more energy-efficient than induction motors.  That's totally unimportant here, though; a waste disposer probably uses a quarter's worth of electricity in its lifetime.  If you don't believe me, look at it this way: a 1-horsepower motor will draw about one kilowatt of electricity.  If you run it for an hour, under load (not just spinning with nothing in it), it'll use one kilowatt-hour of electricity, which costs less than a dime.  Now, think about how long it would take you to put an hour's operating time on a disposer.