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.
at home, i don't bother hanging art – i have mirrors