Ok, so first off: 1080p is a mater of resolution. The 1080 part refers to the resolution (1920x1080), and the second part "p" refers to the fact that the picture displayed is "progressive", meaning that, unlike the "interlaced" standard you get with 1080i, the image in every frame is the whole image, not half an image. In 1080i, each frame that is shown on the TV is really half an image (every other line is removed), but the picture changes so much that the human eye can't really tell.
Bottom line: 1080p refers to the resolution and the fact that each frame is the whole picture. Any graphics card that supports a higher resolution than 1920x1080 (and 2560x1600 certainly is) will support 1080p.
Now, as far as which card to get, it kinda depends on what you are trying to do. If you want to make a HTPC (Home Theater PC) or want to hook this graphics card up to a TV, I would suggest the Gigabyte card, as it supports HDMI right on the card. If you are looking to just game on it, I would also suggest the Gigabyte card (if you have the money), as it has more memory and more stream processors. If you are looking to save a bit of money for an internet/mild gaming PC, then go for the MSI card. It will game perfectly well in most cases and you can save yourself some money.
I own a Cooler Master HAF 932 right now and it works perfectly. I really like their cases, and would recommend almost any one they make.
Oh, and one other thing you should consider re: your new graphics card is what you plan on plugging that card into. If it's a TV that does not support full 1080p, then you aren't going to get full 1080p. Your graphics card will always default to the native resolution of the LCD you plug into it. I personally have a Samsung T240 24" flat panel monitor. Because of its size, I can get resolutions up to 1920x1200 (higher than 1080p), but flat panel monitors that are only 22" or smaller will not be able to display resolutions at or above 1080 (my 22" Samsung 226BW only supports resolutions up to 1680x1050). Just something to keep in mind.
Intel Core 2 Quad Q6600 @ 3.2GHz
4GB Mushkin DDR2 1000
Kingwin Mach 1 1000 watt Power Supply
Asus 4870 x2 graphics card
Gigabyte GA-EP45-UD3P motherboard
Cooler Master HAF 932 case
Samsung SyncMaster T240
3DMark Vantage:
X7241 (all settings maxed)
CPU: 11207/GPU: 7109