Depends a bit on the card and what you're looking for.
As with the Pascal cards, comparing the regular models (Dual&Strix for Asus, SC & FTW for EVGA, not including some special edition cards like EVGA's black edition or watercooled cards), it doesn't matter too much.
FPS differences within 2-4 FPS and temperature differences within 2-3°C is within the performance of the specific chip I'd say.
Although the Strix seem to be a wee bit faster than the FTW from what I've seen. But nothing to make a real difference.
As for EVGA they got a pretty good worldwide customer support while dealing with the Asus support is kind of an adventure from what I've heard.
On the other hand EVGA struggles a bit with quality control lately. There were the insufficiently cooled ACX coolers, the exploding G2 while Asus seems to do better quality control.
In the end it's a lot about pricing. I wouldn't pay 30$ extra for an Asus.
That's my thoughts on the topic