Sure the 7850 1gb will perform a little bit better at 1080p, but you would be paying 40-60 more for a card that is not 40-60% faster and the cheaper 7850s have the same 1gb frame buffer that the 7790 does.
Both the 7790 and 7850 overclock well. Also just a tidbit that in high geometry games with tessellation the 7790 with it being a newer chip then cape verde 7750/7770 and pitcairn 7850/7870 the 7790 newer bonair gpu does 2 tessellation operations per clock vs the other older chip cards 1 per clock.
Since i see you have a Cable card and a i3 along with that big 3tb drive I imagine it is a HTPC. I can vouch for the effectiveness of a hd 7750 his icooler card that has no pci-e power connection and it overclocks like a beast paired with a i3 2120 on a 300 wat psu. Your cx 430 should be plenty for a 7850 but its a shoein for a 7790. My little 7750 does 1080p with no problem just have to go with medium and no AA on hardcore games like BF3 and crysis 3 and I get average 55fps plus since I am not 18" from the TV it looks great. Add the 7790 is 2 tiers up from the 7750 I have"and i am pretty picky" so you should be very happy with it.
But if you feel you need a 7850 try getting one with 2 gb of memory. But i would go with the bargain 7790 you will be happily surprised. Plus you can Overclock it a bit if you want. I really wish the 7790 was around for 100$ when i bought my 7750 for 85$
Happy shopping and gaming.