"Now, I can understand that someone who is young, and with a long life ahead of them, potentially, should be treated differently, in most cases. But prohibiting someone from controlling their own life, or death, is no different than slavery."

I would go with the second statement. The decision belongs to the person.

As for suicide, I have often wondered when it became a sin in the eyes of the church, and if only Christianity sees it that way.

Yes, life at all costs is not a good idea.