I got a pair of GR 4's from TW when they were on sale. I'm used to a more low-to-the-ground shoe and get that with the Asics Gel Game, but their newer generation is too narrow for my foot. Interesting comparisons though...
The Gel Resolution is more built up - by that, I mean that I can certainly feel extra "stuff" under my heel. At least the back half of my foot is farther from the court surface, so that means that there's extra lateral stress on my ankles when I accelerate from side to side (despite the rather substantial heel counter in my GR 4's).
While there's a strong argument to be made for having proper cushioning or shock absorption in a shoe, I've found the most stable and comfortable layout when my feet ride down closer to the court surface and when I also have proper ankle alignment with those shoes. Despite the cushioning in the GR 4's, my ankles have been much better off with a couple generations of the Gel Games - just hoping that some "shoe stretchers" can fix the narrow front end of my sneaks.
So velocity, I'm curious about the fit you're getting with your Gel Resolutions. You're describing what I'd experience if I played in shoes that were too wide for my feet. I used to use some Prince shoes for a while and always wore two pairs of socks, but still slid around inside them a bit... too wide for me.
The other thing that makes my feet more prone to sliding around inside my shoes are synthetic socks. Even with a good fitting shoe, those things are just more slippery for me. If I put a pair of synthetics under a pair of cotton socks, I do better than if I have the synthetic pair on the outside so that they're touching the insides of the shoes. Just my experience - get the width of you feet measured in case you don't know whether they're in the wrong shoes.