Hey, I play League of Legends quite frequently. My IGN is Cheez Bix, on the North American server, if anybody is willing to play. I already have Bitmap (Baka / Wasabikun) added.
Annie is preferable over Ryze to most team compositions at the moment due to her crowd control capabilities. Ryze only has a snare, which has a hopelessly short duration at the start of the game; Annie can potentially stun the entire enemy team... right at level 1.
From a damage perspective, the two champions are comparably similar. Annie is immensely superior, however, where all disabling effects are concerned.
The Ryze re-make that's coming next patch should be interesting, though, and will evolve his character in a manner that will be considerable indeed.