Edit: OK now I went back and created one possible complete set of stats for our two players:
Code:
Player PA AB Singles Doubles Triples Homers Hits Walks HBP TB TB+* AVG OBP SLG OPS wOBA
Jack Slugger 600 503 42 25 2 32 101 95 2 226 323 0.201 0.330 0.449 0.779 0.343
Mickey Slapper 600 574 112 44 6 10 172 24 2 258 284 0.300 0.330 0.449 0.779 0.339
I was able to get very close to the slash lines proposed by SuperDude. There might be other possible stat combinations that match the proposed slash lines.
* TB+ = Total Bases plus Walks and HBP
I did this to get an idea of how many bases each hitter touched during the season as a result of their plate appearances. The Total Bases formula does not include BBs and HBPs.
Both of these players would be solid, above-average hitters in the major leagues, but they would not be anywhere near star caliber.
The OPS and wOBA scores for the two players are almost identical even though the slash lines appeared at first glance to make Mickey Slapper look like a superior hitter than Jack Slugger. Even a huge 100 point increase in Mickey Slapper's Batting Average did not improve his offensive production at all. Their overall production is the same even though they are completely different types of hitter. Jack Slugger has a slight advantage over Mickey Slapper in this analysis. I feel this helps verify my original assertion that as long as the OBP and SLG portions of a player's slash line are equal it doesn't make any difference what his Batting Average is. You don't get any extra production by raising the batting average. The OBP and SLG are what matters. As SuperDude mentioned, knowing a player's Batting Average can help you learn what style of hitter he is, but it doesn't help you identify which players are better.
A player's OBP and SLG are critical to evaluating his performance. His AVG is trivia.