So my take on this is that the two are compared a little more than is warranted, though understandably since Toon Link basically replaced Young Link in Brawl. In Ultimate, the two have very different ways of doing things. If you try to play one like the other, it's going to go badly. Toon Link is a lot more comfortable playing slightly outside of traditional sword range, getting closer when safe and backing off when it isn't. He isn't able to do too much from across the entire stage and can get overwhelmed if the other player has faster frame data and gets up in his grill. Granted close combat is better for him in Ultimate than it ever was, but he still has a short sword compared to others with about the same frame data. What's great about Toon Link is that his whole kit except maybe down-air has amazing synergy. Almost everything can combo into or out of something else at some percents, which makes killing a lot easier as you mention in your video. He also can be quite safe in neutral, thanks to his disjoints and movement speed.
Despite sharing a lot of the same move archetypes, Young Link has quite different game plan. I've seen someone compare him to the space animals, and I think the comparison is apt. He has very good frame data on some of his moves (not so much on others), and can do quite well up close if need be. His projectiles seem (to me, anyway) to be designed more for walling people out and forcing approaches than for combos and confirms. He just doesn't like the fuzzy midrange Toon Link calls home quite as much. He can do okay there, but he can get punished harder for whiffing his projectiles, so its more dangerous. Once he's either inside or out, I think he does fine and can get to those percents where he can get his kills.
Honestly I believe they will each thrive in different matchups. There will be some overlap, of course, but their major strengths change things against certain archetypes. I wouldn't be surprised if Toon Link was better against swordsmen, while Young Link was better at dealing with rushdown types, for example.