Given that you have the budget for a HD7990 I'd say you should look to adding the 290x and 290 to your list if you haven't already.
If Battlefield 4 is all you're looking to do I'd scrap the HD7990, the driver annoyances, extra heat and power consumption are too much of an issue.
Similarly, unless you're comfortable with waiting for the 290x and 290 to get custom coolers or installing one yourself they aren't really that viable an option next to the 780. (Although it is hard to look past the 290's bargain pricing).
The 780 handles BF easy and given a good overclock competes nicely with the 290x and 290 (but ships with a customer cooler), I'd recommend it if the AMD alternatives aren't appropriate for you. Keep in mind that AMD are demoing Mantle in a couple of days and that could shake things up a little bit.