Which batter do you want?

This hypothetical is a little unrealistic, because the GIDP rates for both are pretty arbitrary. I mean, no one GIDP in 20% of their PAs, and almost no one with any significant number of PAs never GIDP (in any league where it's possible to turn DP on someone else at a 20% clip, anyway)

In a realistic scenario where the .400 hitter isn't GIDP 4 times as often as the worst actual player does, he's obviously much more valuable because he'll make far fewer outs. Even in this unrealistic scenario, the fact that he gets a hit twice as often as the .200 hitter will lead to more total bases being taken by the team because runners advance more than one base on a single far more often than they advance more than 2 on a double. Plus the .200 hitters Ks aren't saving him from GIDP to help balance out the fact that he'll produce fewer productive outs.

Because of the way the question was asked, I’m assuming there’s only room for 1 of the players on the roster. Because of that, and because no other information is available, choosing the player who gets base hits at twice the rate of the other is pretty much a no-brainer. This is exactly why no one in their right mind would only use one or two metrics to make a player decision.

Player 1.....not even close.

Most games are either won or lost by a base hit, walk off home runs are fun but give me a kid with a high batting average when the game is on the line.

I'll take the first ballot hall of famer....

I'll take the first guy too.

Not only is he twice the hitter as the second guy, but he's obviously a leader, because when he's in the game, his teammates get on base frequently. The other guy always seems to come up with the bases empty.

As for all those double plays, start calling for a hit and run.  If you're already calling it, stop right now.

(Poor hitter 2 needs some help with the crowd):

Isn't hitter 2 more likely to actually drive in one or more runs per game?  Plus, he is always in scoring position at least once per game.

No, he won't drive in more runs (well, technically he won't advance more baserunners extra bases, which is where the long run value comes from).

If the baserunners are distributed randomly for both, the singles hitter is going to be getting hits with runners on 3rd twice as often as the doubles hitter will, and will drive in more runners because of that.

He'll also get twice as many hits with runners on 2nd, and drive in at least as many of those as the doubles hitter (chance of scoring from 2nd on a single is close to 60%).

Runners do go 1st to third about half as often as the score from 1st on a 2B, but that's balanced by the fact that our singles hitter is getting hits twice as often still. If my math is right net expected bases on 2 1st base runners for our singles hitter is 2.56, and net expected bases is for our doubles hitter on his 2B with a runner on 1st is 2.38. Our singles hitter won't drive anyone in this way, but following hitters will have far more opportunities with runners in scoring position than they will after the doubles hitter.

All that ignores the costs of the GIDP and Ks in the original hypothetical, but there's a runs created formula you can plug all this into, and you'll find that the expectation is still substantially higher for the singles hitter even given the unsubstainably high GIDP rate hypothesized.

Can't score runs if you aren't on base... hitter 1

I'll take the hitter that gets on base more or puts the ball in play more.  You have to get on base to score.   Presumably that is the first hitter.

Hitter one, no doubt.  Those GIDP involve a huge luck factor anyway.  Bet those are mostly hard hit grounders that get to the infielder fast.    Only positioning of fielders and/or placement keeps them from being hits.   Given a large sample size a lot of those balls are actually going to go through and advance the runner.