Adidas or Nike? For me, neither.
I've got very wide, somewhat short feet. Almost no shoes fit me. Shoes almost always press in on my toes and the longer I wear them the more my feet hurt.
Nowadays I wear sandals almost all of the time. If it's cold out or if I need somewhat more foot protection, I've got a pair of extra wide slippers that are awesome.
The only time I wear shoes is if I'm out for a jog or if I'm backpacking - and I have purchased extra wide shoes for those occasions which aren't perfect but are the best I've been able to find.