It's not my choice as it sounds like a shortened version of James and I don't 'do' shortened names. Also, it's fine for a boy but a bit too twee for when that boy grows into a 40 something, 6 foot plus adult imho. I love the name James though.
The problem with the above is that my OH may not agree with me. He's one of two James' in his immediate family and so is known to all as Jamie!
My boyfriend's brother is called Jamie and I hated it from the beginning. TSO, my boyfriend's mum actually used the name BECAUSE it can't be shortened to anything else, which is crazy considering it already IS a shortened version of something!
go with James - Jamie is cute, and cute is great for a baby for a little boy, but a grown man going for a job interview might be better with James. You can introduce him as Jamie if you like, it just gives him the chance when he's older and doesn't want 'cute'.