manddy123 :
I'm a little biased towards Gigabyte as i've always had their products and never had a single problem with them.
But that's just my opinion on it.
If you want facts,
Zotac:
Base: 1771 MHz
Boost:1911 MHz
Gigabyte:
Base: 1721 MHz
Boost: 1860 MHz
Although gigabyte is a bit slower, those 50Mhz won't make that difference in terms of FPS gain, so i wouldn't worry about it.
So, it mainly goes within your own preferences, get the one that you think is best looking/fit more properly in your pocket as both will have the same performance overall
I wouldn't get the AMP Edition if you are set there. The AMP Extreme is so much better. The AE is the fastest 1080 out of the box and you get some great performance out of it. If I'm being honest I hear the AMP has overheating problems as well.
Zotac is a great company and I love my AE, but their fan profile sucks. My AE was constantly overheating and THROTTLING on WoW, because of the crappy optimization, so my GPU was being utilized at like 100% for hours at a time, with full boost to over 2GHz. The fans don't even really kick on enough to do anything until about 50C and they still don't do enough to keep it cool, then it hits 70C by the times the fans really kick on and by that time you start losing performance. And this is on the EXTREME. I set a custom fan curve on MSI Afterburner and now it runs very cool and very quiet still (Usually below 40% speed and under 45C, even in WoW).
I have no experience with Gigabyte stuff but if you are stuck in your price range, get a different card than the AMP, but if you can, get the AMP Extreme.