Ok, I have a progressive team in the deadball era (so little power hitting just to help think this through), and the first two starting OFs are near superstarts.
Third starting OF goes to either of two players:
One hits .234 with an OBP of .380
The other hits .290 with an OBP of .333
Neither hits with any power and neither has any remarkable SB qualities. Around a tie defensively. Both have good PA.
So, do you got with the traditional criteria of batting average - a substantial difference between .290, a hitter that could hit third, fifth or sixth, and .234 - or with OBP - a substantial difference between .380, which would be a player I could put near the top of the order, and .333, which is respectable but nothing to write home about.
How seriously should we take OBP as a main criteria. I think this one is a good test of recent ideas about baseball strategy.