For me it's and I think it will always be asics for classic running. For trail running, I'm using Lafuma, a french brand. Normally, we don't have to choose a particular brand. I think the best thing to do in order to have the best running shoes is to find a vendor with good knowledges. After that, considering your type of running practice, how many hours a week you are running, and your goals, the vendor will guide you to a specific shoes, no matter the company.
adidas and nike it was better shoes, or kappa maybe, but i thing nike it's more better than adidas and kappa.
For me it's Nivia sports shoes, it's cheap and best, not that cheap, still cheaper than addidas and Reebok.