A lot of pros that use Tourna (and a LOT still do) often have leather base grips, so you can't really compare.
I've also had hydrosorb and used them, both new and worn out, with tourna grips over. I see no difference.
If you want it softer, maybe wrap the hydrosorb a little looser, or put 2 overgrips on. But you'll basically loose the bevels/edges with 2 overgrips on top of a hydrosorb (or any synthetic base grip).