It is better, because we're not accountable to a higher power, we're accountable to society and each other. Children need to be taught compassion, not that an all-seeing judge in the sky is examining every second of his life and gets to decide their ultimate fate.
If Billy is considering stealing Mikey's bike, which of these alternatives is better, more 'moral'?
"I'm not going to steal it because god will punish me"
or
"I'm not going to steal it because it will cause Mikey suffering, and he doesn't deserve that"
I agree with you that empathy would do all of mankind a lot of good.
But let's be realistic. Mikey is not weighing good vs evil, he's weighing punishment vs reward.
If he can steal Mikey's bike, get satisfaction out of it, and not get caught or punished, then he will do it. That's how humans are.
It'd be nice if humans were different, but they're not. And quite frankly, without a god, there's no reason they should be. The well-being of everybody is fine and dandy, but it doesn't really compel people to look beyond their personal suffering and fragility especially since the well-being of everyone is a fantasy and their personal problems are real.
An objective universal law or a spiritual mindset can get people to look beyond that, but when it comes down to it, if there is no god, there is no reason for a person not to hoard all the selfish pleasure they can get out of this life even at the expense of others.