ryuk has no battle stats and the only time shown to fly was very slow.
Ryuk has no combat feats so we can't exactly comment on a fight. And Ryuk is a mid level Shinigami with no crazy powers to speak of like the higher level ones. But if he uses the Death Note on Ichigo, I guess he would die since he is still human (sorta). But there is also a chance he would just go full hollow and destroy everything if he died. So I'm not sure. I'm not sure of how Bleach and Death Noteverses would match up. Oh, wait. Ichigo could kill Ryuk before he gets the chance to write anything. So I believe the winner would be Ichigo.