Who does inuyasha pick kagome or kikyo?

InuYasha never actually picks. It's a complicated situation. In the end Kikyo dies for good, and does not come back to life. So, he's left with Kagome. In the end, InuYasha and Kagome get married, but who knows what would've happened if Kikyo lived? I think he would've chosen Kagome because their bond was greater than his bond with Kikyo.

In the end, he never picks. He is merely left with no choice but to stay with Kagome. Although, he will never forget Kikyo.