STR : Very slightly increased damage (wpf and speed bonus versus PS), more if you play like a retard. More HP and significantly better survivability if you are not mobile. Also, you don't lose much wearing heavy armor when you are already slow.
AGI : Much better foot acceleration, slightly increased top speed. A potentially much higher survivability through dodging projectiles, cav and avoiding being ganked. A decent level is usually required to pull off any dirty engine abusing duelling trick.
In the end, STR and AGI are both balanced with each other but situational in their own way. What you should use depends on your playstyle, not what other people say.
Patient and defensive players will probably prefer STR chars because they don't feel an urge to kill their opponents quickly, and usually don't need it because they stay safe, while twitch centric and aggressive players will prefer AGI chars for their capacity to bring down enemies quickly and using their speed to get a tactical edge.
STR is forgiving for duelling errors like missing a block, but AGI is forgiving planning/awareness errors with it's wonderful dodging. Also, the longer your weapon the less you have to care about all of this because you have to block once in a blue moon.