My opinion...
I've hiked some nasty stuff in running shoes (Class 3, 14k+ feet). If you do it all the time running shoes won't hold up, but for the occasional trip they are great. Biggest advantages: cheap (you probably already own them), already broken in, lightweight, flexibility (personal preference)

Hiking shoes are better IF you use them a lot and get them broken in, otherwise they are just a recipe for sore feet/blisters.
Advantages: durability, stability (personal preference), ankle support/protection (if you get boots)