The short answer is: they don't.
You can quite happily raise a whole bunch of Hero Chao in the Dark Garden and vice versa. I use the three gardens as follows: Neutral for working in, Dark for storing eggs and baby Chao, and Hero for storing evolved Chao with maxed stats (the realm of champions, hehe). In my Hero Garden there are usually two or three Dark Chao in permanent residence, including a Dark Chaos, and none of them have ever shown any signs of unhappiness. And when I bring my Hero Chaos to the Dark Garden, she makes straight for the pool... o_O
The long answer is: living in the Hero or Dark Garden may have an effect on the alignment of a baby Chao. I've seen a report of someone who made eight new baby Chao in the Dark Garden and then stood Sonic in the water for several hours. When he came back, all the Chao were Dark. Since he wasn't feeding the Chao, this could possibly be a neglect issue too.
In practice, I can't see this being an issue. I've never seen my Chao change their alignment naturally, even in the Dark Garden, and if you want to raise Heroes there (or Darks in the Hero Garden) all you have to do is care for them with the right character.
The only reason you'd want to worry about the Garden's effect on your Chao's alignment is if you're trying to make an S-rank Chao by forced aging (see section on S-rank breeding under Advanced).