Who is best, ASUS or EVGA and why?

Brand alone is not going to dictate which are "better". Some of the models are clocked higher (ROG Strix from ASUS among others, SSC+ ACX etc from EVA).

Look to the specific model of a card to determine which would be the "better" fit for you. I don't think you'll find a definitive one is better than the other when comparing ASUS and EVGA.
 
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