I got 6.03 after searching a lot for which is best. I spent hours searching hundreds of posts on various forums and websites, and most seemed to say this;
With a 6.01, you get less air around the BB, so more force behind it, increasing power, but giving less accuracy than a 6.03 (debatable if it's more than a 6.08 stock).
With a 6.03, you get more air around the BB, so less force behind it, still increasing power (from stock 6.08 barrels) and increasing accuracy more than a 6.01.
Also, I've seen a few times before from PDI or LayLax (can't remember or find it) them saying that wider is best for accuracy and thinner is best for power.
Which brands are you looking at?