I own an UP Shift, but my buddy owns a Grip that I've played around with a bit. They're both amazingly quality bags with tons of features. So it's not like one is inherently better than the other. They do fill different roles, however.
My first bag was the cheap Academy Magellan for $30. Great bag for the price, but clearly not of the most quality build. I ended up wanting a new bag because I was only using ~10 discs per round and if I took out a significant amount of discs from the bottom compartment, they started falling over. I settled on the shift because it didn't matter if I loaded it with 3 discs or 15, they staid in place and were organized. Also, the single water bottle holder in the middle of the bag made the weight distribution much better.
You know what the Shift doesn't do well? Carry a ton of discs. When I'm doing field work, I'll try loading it up with 20 or so discs. They may fit, but they're hard as hell to get in and out. That's fine for field work, but wouldn't work well at all for a round. Also, if you drink enough water to warrant a second bottle, you'll have to put your second bottle in the large interior pocket of the Shift where it will be able to roll around.
So it really comes down to what you want from your bag. Lots of discs and/or water? Go with the Grip. Less discs so you can carry a lighter load? Nobody does it better than the Shift (in my opinion).