Apparently the HD 5000 series cards have a o/c limitation, apart from the ASUS versions, I'm not sure if it applies to the HD 5770. Either way, go for the card with better warranty, if they're the same, go with the ASUS card.
I have used both Asus and MSI ATI based video cards and have had great success with each. As Lmeow suggested, comparing the warranties is a good idea, as is comparing the cooling system of each vendor's card.
If you want a quiet card, look at product reviews of each for comparison. Newegg has one of the better review systems on the market and a quick scan of current reviews can let you know if a particular vendor's solution has problems.
Both vendors make good stuff. If still a toss up, I would go Asus as well.