Birkin. Though the Lindy is a great bag, if you get the Lindy, you will, likely, still lust for the Birkin. You will end up purchasing the Lindy and you will have to start saving again for the Birkin because it sounds as if that is what you really would like to own. Good luck with your decision!
if like you said Lindy suits your look more then maybe you should get Lindy. If you lust for more in time to come, you can spend on a Birkin. It's more which bag speaks your style at the point in time rather than simply a must have bag nthat dominates your decision.
Good luck with your decision!