It is the strength, flat out, though there are instances dragon slayer is better. Example, Wendy being able to heal physical wounds and someone's energy while Chelia can only do the former with her magic.

Also, remember that Dragon-slayers cannot eat a God-slayer's flames, probably because of this power difference.

Where Devil-slayer is in the hierarchy is rather unknown. Until a devil-slayer fights a dragon- or god-slayer of the same type, it'll likely remain a mystery, though I'm sure it's at least stronger then dragon. Sometimes I think the battle between Gray and Silver revealed too little.