I'm only familiar with 2 of the 4 (5) grips you mention – Head and Babolat. The Babolat VS feels a bit thinner than the Head Tour, both wrapped the same way.
As an alternative I think Vantage leather is pretty thin, but I'll have to go and check my unwrapped ones to be sure. You can't go wrong with Bab VS, though.
Prince Tour 100T ESP \\ Tecnifibre Razor Code 17