JG role better than lane roles?

That's really just an opinion. There is no right or wrong answer.

Jungle is basically the early game carry for the team, as opposed to the expectations of midlaner mid game carry and adc late game carry. Or at least carry in terms player the team plays around.

As the early game is the only part of the game that is always played, yeah probably. Having a lackluster farm jungle on one team and a dominating jungle on the other is often the quickest way a game gets decided. However jungles do get less gold and exp typically and will not have the presence of a laner late game, usually.

If you're talking about climbing, then it's support.

I personally prefer Jungle, but jungles get less gold less experience and more responsibility as a trade-off for more safety and larger map presence.