I had an OiOi CarryAll which was great - except that it had plastic zips, which eventually broke - didn't take kindly to being routinely stuffed to the seams. Loved it though.

Hated the messenger one I got, because if you're trying to get to things one handed, the flap keeps falling down.

Now have an Isoki one (without the carry-all style straps, just the one big long strap), and I love that, the downside to that is that it's made of canvas so it's HEAVY (Falguni DID warn me!). But, considering I have 2 kids and pack like I'm travelling overseas when I'm really headed to the shops, any bag is going to end up heavy. It's got metal zips, so should work out tougher, and I talked to the owner who said that if anything goes wrong to bring it back to them, cos they don't want unhappy customers.
I also unzip the bottom off the Isoki if I want it to be lighter, and keep the nappies in the main section of the bag, in one of the separate bags.

Oh, and I use cloth nappies, and the Isoki, and OiOi CarryAll fitted nappies for both boys just fine.
Let us know what you end up with! I love bags.