

Ashlee Simpson - she of the bad haircut, nosejob and coattails of Jessica.
Avril Lavigne - abuser of ties and eyeliner. So punk rawk.
Vocals
Ashlee - If it wasn't glaringly obvious enough, the Superbowl lip-syncing disaster exposed Ashlee's talents for what they are; ie. non-existent. Utilizing synthesizers heavily to distract from the less than savoury vocals, Ashlee has made 'sing-thesizing' into an art form. She can't hit the high notes right, veering closely to screeching and screaming in the chorus of 'Shadow'. Hell, if she had to rely on a back-up track just to get the low notes right, you know it's a long time coming before she's breaking any records at vocal prowess.
Avril - Apparently started singing at church since young. Did that help? Well, apparently not much. In her past albums, she's proven to be just a tad better than Ashless at this singing gig, which isn't saying a lot. I suspect that somewhere somehow Avril is living a second life. Her contribution to the Eragon soundtrack, seemed to promise a more mature sophomore album. For all it's power ballad-y instances in 'Keep Holding On', Avril mostly managed to tack on the power in her warbles. Then 'Girlfriend' was released. Right.
Ashlee = 0, Avril = 1
Music
To look at it superficially, Ashlee and Avril's music deviate slightly in such that the former is more rock and the latter, more punk. Essentially, both pop stars are just that; pop. So drawing a difference between the two is a lot like drawing a line in sand during high tide. Nonetheless, Ashlee's back up band uses arguably more bass and riffs ('Boyfriend'). I mean, they would have to make up for the lack in vocals in some way after all. Avril on the other hand, keeps the verses and rhythm punchy ("He was a boy/She was a girl"). Of course the hardcore punks are cursing plagues at Lavigne's house for her blasphemous 'tude. But at the very least kids below 4'9'' will be exposed to punk, or punk-reminiscent music to be more exact, without the sex and drugs that usually come attached with that genre of music.
Ashlee = 1, Avril = 0
Image
Ashlee - At the start of the career, to step out of her sister's shadow, Ashlee died her blonde hair black and assumed a rock persona. She was the chocolate chunks to Jessica's white vanilla in the Simpson gene pool, or so it seemed. For the most part she did successfully carve out a career separate from her sister's. And then she went blonde. And fixed her nose. And became the spokesperson for Skechers. And all of a sudden she's looking like a less-tan, less-chesty version of Jessica Simpson. One Jessica Simpson in the world more than fills our vapid bimbo pop star quota. Do we really need another bland blonde robot? Interesting to note that Ashlee's original hair colour is blonde. Ashlee is also currently dating Pete Wentz, abuser of camera phone and bassist/song-writer for Fall Out Boy. Do you think they maybe pool money and bulk buy eye-liner? Cause that stuff ain't exactly cheap. Especially if you get the waterproof ones.
Avril - After showing the pre-teens that girls can wear neck ties too, Avril continued her trend of baggy pants and white wife-beater for a while. It was so rawking, the fashion world collectively fell into a boredom-induced coma. Then at some point she dis-owned her tie trend and put away the hair straightener. She took the pink out of her hair and started dressing up. Voila, one awesome model under the facade at your service! What she lacks for in vocals and personality, she makes up for in bone structure. That girl puts Derek Zoolander out of business, I tell ya.

Of course, come 'The Best Damn Thing', the straightener, pink and punk rawk is back with a vengence. Regressing to familiar territory may be great for album sales but awful for a bystander.
Ashlee = 0, Avril - 1-0 = 0
Personality
Ashlee - Blaming the band and "acid reflux" for your mistake just isn't cool. However, Ashlee's music videoclips earns her back whatever points she lost for flubbing responsibility. Have you seen that girl dance? For someone who apparently did ballet when she was younger, the girl has the grace of an elephant on rollerskates. No really, it's like she's having random seizure attacks.
And because I myself am one with the spazzy dancing, I can't hate on Ashlee for that.
Avril - Yeah, we get it. You're bad to the bone. We saw it in your music videos, we saw it in your interviews and the paparazzi saw it first hand when you spit at them. Yawn. Next!
Ashlee = 1, Avril = 0
Final tally
Ashlee = 2, Avril = 1
Ashlee Simspon slips in to win the battle of the can't-sing-"bad-ass" rawk princess. The world continues to turn on it's axis.