In some ways, you're right - it'd kinda fit in both. That said, chimney sweeps were mainly children, because, well, they were small enough to fit in the chimneys and not get stuck. They were also easily replaceable.
That said, I think this poem fits in Songs of Innocence more thatthan Songs of Experience because it's all about that loss of innocence. Children are supposed to be carefree and, well, innocent. They're not supposed to know the dark underbellies of the world.
In this poem however, he's contrasting this idea of childlike innocence, which is what we expect, with the idea of the needs of adults (clean chimneys) stripping that away for their own ends. Death is really their only way out (as we notice in Tom's dream:
And by came an angel who had a bright key,
And he opened the coffins and set them all free;
Then down a green plain leaping, laughing, they run,
And wash in a river, and shine in the sun.
It's only by dying in these horrible conditions that they will get their childhood back - in a sense, they'll regain that innocence upon death. They'll get to be the free and playful children they couldn't be in life.
Also, the last line shows that even though they leave in a bleak, dark world that will effectively destroy their innocence, they still do keep it in a way. (At least Tom does):
Though the morning was cold, Tom was happy and warm;
So if all do their duty they need not fear harm.
Even though he's just dreamed of death being his only escape and his only real chance at innocence, he still retains some innocence about the ways of the world, as he believes that if he just does a good enough job of being a chimney sweep, he won't come to that deadly end. That's a somewhat innocent and naive way of thinking of the world, even though he's constantly living in a situation that should teach him the complete opposite is true.
So that said, I think this does fit more as a Song of Innocence rather than a Song of Experience because even though in some ways these children should have no innocence left, they do, in that resilient child sort of way, push back and retain it, even though the world is trying really, really hard to disabuse them of the entire notion of innocence.