I have all 3 versions of the 360 grip and they are virtually identical. The difference is mainly cosmetic. Just be aware that there are different core sizes. Titleist's standard is to put a 580 core grip on a 600 shaft which makes is slightly oversized (equivalent of a 600 grip on a 600 shaft with 1 extra wrap). The Golf Pride TV 360 is only available in 600 core so it may seem undersized if you don't build it up.

As far as the irons go, I believe Titleist started using the 360 grips only on the 716 series of irons so if you tried different models and they felt different it might be the the shaft diameter of the stock shafts was slightly different making them feel different. 714 and earlier series used Titleist Tour Velvet (non 360) on the irons.

Hope this helps

Thank you so much for the response! Makes sense. I understand about grip size and was wondering where can i get .580 TV 360s?

I was in Dick's recently and the grips on the Titleist 917 hybrids were golf pride tour velvet. They were black/white and looked very similar to a Lamkin grip. I can't find these grips anywhere on-line. Are these grips for sale? Thanks.