I've both. The Birkin is a more casual bag, as it's essentially a tote. The Kelly is more dainty and classier one of the two. The Birkin is a great bag but I find that I use my Kelly more, as it's lighter and I love the classier look, especially when I need some perking up. With the souple style, the Kelly can be more "casualized".
I got my Kelly 1st, then the Birkin. Thought I'll be totally in love and satiated with the Birkin. Recently my Kelly passion has been reignited. Think it has something to do with pictures of V.Beckham and her rigide black Kelly! Also, there seems to be more ladies with Birkins than Kellys.