Deciding between 2 cards

The ASUS one will always serve you well it has a much better heatsink/fan than the Gigabyte one, plus faster memory. There is simply no contest when it comes to motherboards/GPU ASUS is king.

I would spend another 10 dollars and get the ASUS HD 7750 as that card will run circles around the HD 6670 model.
 
The more expensive 6670 come with GDDR5 memory, so you will get faster performance if you get that rather than the normal DDR3 version (the cheaper one). To be honest with you I'm going to go with the GDDR5 version to get better performance. I always recommend the person to get better cards when they can afford it (except the other card has better rivals in the same price but better). Maybe you can take a look at this? This is a 6670 GDDR5 version, but only $90 with free shipping (the other one is $92 with $8 shipping).

http://www.newegg.com/Product/Product.aspx?Item=N82E16814102958
 


Well most of it is true, low profile rarely equals performance. But new models such as the HD 7750 can come in low profile variants and they pack the same punch as the regular models. I would skip the HD 6670 its time is over and it isn't a flexible card. The king today when it comes to low power(wattage)/solid performance is the HD 7750 and it runs circles around the HD 6670.