I don't think they look alike, but it seems that some people including Perez Hilton think so. I think the photo being black and white makes them look more similiar then usual though. I think comparing the two is like comparing little league baseball to MLB. No comparison.

http://perezhilton.com/2008-07-24-theyre-not-the-same-person

Katy Perry kisses girls and makes mindless commercial radio friendly crap. Music spawned from Hot Topic.

Zooey Deschanel has a very good voice and has put out some good music so far. 

Glad some people get it. Katy Perry is w.0. She's so w.0 she's not attractive.

Listen, I like a pretty lady as much as the next guy. And, more specifically, I like a brunette with bangs more than the next guy, but this is getting WAY out of hand. You look like what would happen if someone dipped Zooey Deschanel and a funfetti cupcake in a vat of toxic waste and topped it off with a few hundreds pounds of high grade trucker meth. Literally! You LITERALLY look like you were made not from man, but from a Ninja-Turtles-origin-story-esque mistake.

...

...

http://dealbreaker.tumblr.com/post/673786289/you-are-katy-perry-listen-i-like-a-pretty-lady