typically, unless you have very sticky tires or a very good driver, an auto will beat a stick off the line- but normally not by much. if we are talking about the auto transmissions in most hondas/small compacts, a stick shift will give you better performance, and slightly better economy, for a couple of reasons. first, your avarage compact car auto transmission has either 3 or 4 gears, and most manuals have 5. also, you loose power in the torque convertor, and the computer-controlled shift points on many newer autos sacrifice accelleration for economy.
having said that, it's important to remember that not all transmissions are created equally. the 5-speed racing transmissions in the older Ford Mustang 5.0 GTs were bulletproof, and would run like hell. the auto transmissions in a lot of old hot rods were very well made, and would reliably beat their stick-shift counterparts down the strip.
for me, i prefer a stick- it's not much more work, it's more fun to drive, and i havn't been able to destroy one yet. i've killed at LEAST 3 automatic transmissions, and the 3 manual ones i've had have all survived me. granted, the honda needs a new clutch- but it's got 130+ thousand miles on it, so i'm not doing too bad.