Far more of the came here than went there. Platt, Ince, Gazza and Souness all come to mind as being fairly successful there. Can't think of many players coming into their prime moving there, generally those who'd had a good career and were slightly past it.
So what you're basing this 'better record' upon is a bit vague and hardly going to be like for like.
Fair few Brits have gone and done a decent job in Italy I think. Those that you mentioned. Ray Wilkins has a spell at Milan too, and Gary Charles I think his name was scored a shitload for Juve once upon a time. Robbie Keane’s spell at Inter was short but I don’t think he was as bad as made out either.