[quote=@The World]
<Snipped quote by Nimda>

I personally like having the Sharingan, but that's because I have the advanced version that you wouldn't be able to get, unfortunately. If you mean specifically between the Byakugan and Tenseigan, I prefer the Byakugan for its enhanced sight. 
[/quote]

I think I'd choose the Rinnegan and Byakugan, unless there's a hidden drawback that I missed.