Hello there. Here is my Personal experience with both trademarks.
Asus is a very quality producer and they tend to take out their products to the market with a stricly careful quality control tests. Its kinda difficult to find a single asus products (from 3 years ago to now) that randomly dies.
The materials and designs are generally good to exellent and their product distribution is nice at the point you can find the same card in almost every store. It has one big dissadventage against Gigabyte and its the price cost. Asus products tends to be way more expensive than Gigabyte products.
On the counterpart we have Gigabyte a well known trademark for its price quality stuff, All their product versions are even cheaper than the Reference ones while maintaining certain good quality that makes them different from any other trademark.
Their designs are mostly cooling efficient BUT not silent enough. They have some nice looking too (even when i am not a big fan of them) and as i said before, they strong point its the price-quality of their products.
Conclusion: I would just pick Asus over Gigabyte if the money its not problem for you, in my personal experience asus has never let me down. So i repay them by being a loyal customer (Whenever their products dont suck, certainlly not the case for now). Overall both cards perform the same, But as i said before. I would go for the Asus over the Gigabyte if the money difference is not a problem.