I too have a 6s Plus running iOS 9.3 Beta 1 but in my experience everything is running smoothly and with no delays whatsoever. Considering it is beta software (and let's not forget it is only beta 1) it is very polished and with absolutely no slag (stutter+lag). OP: Since it is not clear how you upgraded to 9.3 Beta 1, something specific to your update may have not come over cleanly. If behavior continues, I would revert to the original iOS installed on your iPhone. Who knows, you might have a faulty iPhone.