Fearow isn't the best Pokemon in the world. He is outclassed by Dodrio is most ways, as well as by most other Pokemon. He's fun to try every now and then, but he's better off where he (and his little brother, Spearow) is: in the cartridge game, attacking you whenever you go in a small patch of grass.
Okay, so Fearow has nothing on Dodrio, and I mean nothing. Overall, what separates the two is the fact that Fearow has 10 higher HP, 2 higher Special, 10 lower Defense, and 40 lower Attack. Also, Dodrio gets Body Slam.
However, Fearow does get Mirror Move, which is cool to dish back something like Earthquake to a slower, Rock-type Pokemon (hey Onix), or even the odd chance that you switch into something like Tangela and the Sleep Powder misses. Drill Peck should probably be used over Double-Edge, mainly since Fearow is fragile without taking recoil damage every turn. Double-Edge is more for those Electric-types if you can predict a switch.
You could possibly give Fearow Agility to fight through any paralysis it encounters. Also, if you don't like Mirror Move, there is always Mimic to try. Maybe you could Mimic Explosion from Muk.
Checks and Counters
In OU, the premiere counters are Rock-types (Golem and Rhydon) and Electric-types.
In UU, Omastar, Kabutops, and Onix are the best counters. Pokemon like Electrode and Magneton would also counter Fearow well, being resistant to Flying-type attacks and having the ability to cripple Fearow in turn with STAB Thunderbolts.