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I think +1 str and +1 ap have the same effect in dishing out damage (only from observation, no supporting data). You can get a lot more attack power over strength, but then think of all the skills that raise easier if you have a high strength.
Raising strength absolutely helps out other stats, but when it comes to absolute damage results, stacking attack power over strength is the way to go. AP will bust through even the best armor and is cheaper to build then strength. And it works great for low strength gladiators that cannot stack enough Strength bonuses to be effective.