There are only a handful of AM3+ mobos with the proper VRM design to handle the FX-9000 series CPUs. I believe that Gigabyte only supports the FX-9000 series on the 990XFA UD7 so I would NOT recommend trying to run it on the other mobo models.
Asrock has two mobos with 12-2 phase VRM designs that are both approved for FX-9000 series, that being the Extreme9 and the discontinued Fatality Pro. Testing has shown that either of these boards would serve you well.
As I have posted if this forum before, I have used all of the major brands of mobos and IME the Asus mobos in general are not as reliable as the Asrock or Gigabyte mobos and the Asus models are often RAM sensitive compared to other brands of mobos. Other folks have shared the same experience. With Asus using several companies to manufacture their mobos you never know what you are actually going to get when you buy. The only two mobos that I have had fail in 20+ years of building highend PCs were both Asus.
Asus gets lots of hyped reviews from supplying hand picked mobos to review sites but the Asrock and even Gigabyte mobos tend to overclock as good as the Asus and some times better. At one time Asus was the gold standard in Asian manufactured mobos but that was 20 years ago when they only sold to OEMs, before they started selling to end users via retailers. With various companies producing their mobo products the quality varies considerably.
Whatever mobo you decide to go with, make sure it officially supports the FX-9000 series CPUs or you'll likely end up with the VRM circuit overheating and throttling the CPU or burning itself up. No one will warranty the mobo if you burn out the VRM circuit.
You'll need a highend HSF or water-cooling to cool the FX-9370. I don't recommend Closed Loop Coolers (CLCs) as independent testing confirms they have poor thermal efficiency and the inescapable water leak liability. Unfortunately good open loop water-cooling systems start at ~$195 and go up and they too can and do leak, with the possibility of damaging all of your expensive PC hardware.
Building a reliable PC involves more than just assembling the parts. You need to be able to configure all of the BIOS settings appropriately. This can be quite involved and frustrating as it can require a lot of trial and error with stress testing. It is however often the only means to get a 100% reliable PC.