Obviously for aesthetics and maybe thermal temps it matters. But does it matter enough that it's worth paying more? What about the manufacturer boasted "over clock"? Is it really that big of a performance difference? Let's find out!
Sometimes you get a redesigned pcb, with better power delivery, next to a better cooler, lower temps, less noice, so yes sometimes a bit extra is really worth it.
In my experiences they are more or less the same. With certain cards like the HIS IceQ, it's certainly a better binned card, so the overclocking potential is greater than that of the ASUS. But in general for the avg consumer it makes no difference. The only thing to look out for is if the board partner uses a different memory type or memory bus width. For example you will see some GT1030s with GDDR3 and some with GDDR5. The board partners selling the GDDR5 model are the ones you would want to choose, as the memory type is newer and faster
Cooler is big and heavy then PCB will be bent in the long run. I have ruvy OC version pci e 3850. It's working bent. If I fix straightforward its not working.