I went from tri 480s to dual 680s and it was not much of an upgrade. Dual 680s were actually slower in some older games, but faster in newer titles. Because you game at a high resolution I would avoid 680, 770 from nvidia and 7870, 270X from AMD along with every card below those levels.
So if you want to really feel like you've upgraded I would go bigger than just a 7990, which is probably around where dual 680s are.
I would want to get rid of those horrible 480s no matter what though. A real upgrade would consist of a few options and you'd have to wait a week till the new AMD cards come out to get a good comparison. I would say you almost have to go multi-GPU to really feel it. 780 SLI, R9 290 Crossfire, R9 290X Crossfire would be what I would look at. All of which are more expensive than a 7990. To stay in your budget, 280X Crossfire is probably the best and only option. I would prefer that to a single 7990.
Balancing price and performance and raising the budget, R9 290 Crossfire would probably be the ideal choice.