Gerry Chester, who was there, tells us that in most Italian encounters with the Tiger the Churchill came out on top, and the Pz.IV was actually seen as the greater threat by British tankers in that theatre.
I could never quite believe the return rails on the Churchill (but then there's many things about it's development process I find hard to believe
). If I recall it was a solitary Dieppe Churchill that was modified so, it beggars belief that no British designer considered rollers during any of it's long development and the subsequent rework programme. It's said the gains in speed were marginal, but the stress and wear on the track was reduced greatly.