fielding matters a lot, lets look at range as an example.
you pay to draft an A+ range fielder and he gets 20 + plays (turns 20 hits into outs)
I go cheaper for a D range fielder and he has 20 - plays (turns 20 outs into hits)
20 hits one way or the other doesn't sound like a huge amount, but if you look closer it is. a guy who hits .300 in 600 at bats got 180 hits. add 20 hits to that and he hits .333. take 20 hits away and he hit .267. that's obviously worth quite a bit.
in this specific case i would expect your team to turn more double plays with the better fielders on average, but what you're mostly paying for with fielding is fewer errors and more hits turned into outs.