I assume you're referring the the ASUS Strix 780 6GB. As stated, it will not work, I think the Strix will downclock to 3GB's of vRAM, I could be wrong and it might not work. Your best bet is to go with two 780Ti's, it will crush games in SLI. Crysis 3 at 1600P is going to kill your frames though. Expect 30-40 and expect microstutter to be evident as any Crossfire or SLI setup that isn't getting at least 45-60 frames plus is going to have visible microstutter. I can vouch this, I ran two 780Tis in SLI (about to in a few days again when my PNY Enthusiast aftermarket cooled 780Ti's come in the mail) and currently have a 290x crossfire. SLI is MUCH better about microstutter, though. Stay above 45 frames and you'll never notice, and 30-44 it's not going to be bad. Crossfire has evident microstutter at anything under like 55 frames. Take that into account. Honestly, if you want 6GB's of vRAM and performance a Titan SLi (Costly as hell but it'll get you there) or a GTX Titan Z (Not even worth it, just mentioning it, two titans would be better AND cheaper) would be optimal. Or you could go with the 290x at 4GB's. But honestly 3GB's of vRAM is a nice, good spot to be at right now. 4GB a bit overkill unless you play 4K and 6GB+ is straight up not needed.
My recommendations if you HAVE to have the extra vRAM.
GTX Titan / GTX Titan SLi (Very expensive, the performance is the same as a 780/780ti (in the middle really) but you get extra vRAM and the Black Edition reference card is SEXY)
R9 290/R9 290x/R9 290 CF/R9 290X CF (4GB vRAM, if you go with the 290x crossfire and overclock the cards a little you can have 780ti performance and 290x vRAM. A 780Ti overclock will always win in performance, though. Plus NVIDIA has superior drivers, but for price for performance the 290x is the way to go)
R9 295x2: In my opinion this is the single best graphics card out on the market right now. You get GTX Titan Z performance for only $1000 and it comes stock with liquid cooling. Price of one Titan, Titan Z performance, 4GB's vRAM (4GB mirrored, not 8GB) and the kicker, FACTORY liquid cooling. I love this card and wish I owned one. Hell, I wish I owned two! There's no better graphics card out right now and after it was cut to $1,000 this thing is a beast and it's cheaper than a Titan with Titan Z performance. You'll take a 2GB less vRAM hit, though.
GTX Titan Z: I only recommend this if you HAVE to have an NVIDIA card and you have three grand to shell out. This thing is a GREAT cart with a HORRIBLE price, so I'd never directly recommend it.
Otherwise, a 780 Sli will do just fine. Overclock them a nice bit and you can get close to 780Ti performance. You WILL be held at 3GB vRAM unless you come up with a second Strix. Two Strix cards in SLi would be very nice though.