Are there big differences between the MSI, Asus, and Gigabyte 770's? Is there a reason to wait for one to go on sale, or pay a little bit more?
They're all about ten dollars apart.
Not really. One card's cooler might be slightly better than another's, you may prefer the looks of a certain card, or you're loyal to a certain brand, but they're all really good so you should probably go for the one you can get cheapest. You could also read reviews and round ups for the 770's and see which one appeals the most to you.
Gigebyte has the best cooler by a small margin, generally you don't want to pay too much more for one over the other though.
Warranty is another issue. Apparently Gigabyte has the best RMA service in the UK for instance.