Str doens't really help against many enemies. Even if they were using a hammer, your str wont save you from getting stunned by those hits you'll take, when agi at least helps you to stay away out of their reach. Getting stunlocked will kill you anyways, no matter what stats.
Str is important when attacking back, while agi helps to avoid swings. In STR focused NA servers, you'll need less agi since your opponents will be slower.
On AGI preferring EU your opponents will be fast aswell, so you need to able to match them in speed or get ganged.
And, if your opponents are noobs, like Digglez suggest. Go for str so you can kill them faster.
However, if your opponents are just as good as you are, and you have too str based build. You will get hit and stunlocked by their simultaneous swings. This is where STR and IF will only help you by letting you get hit one more time before you're dead.
STR allows your attacks to do more damage.
Agi makes you faster. You'll be able to avoid getting ganged, and ganging enemies is easier for you. However you'll deal less damage.