I recently watched a video by Melee player/commentator Toph, where he goes over a Melee "tier" list by another player named Ginger.
In it, Ginger ranks the characters not by how strong they are, how likely they are to win a tournament, overall matchup spread, or any of the stuff we usually think about. Instead, it's about where characters fall on a spectrum between what he calls "essence" and "fill."
The video mostly explains what those terms mean, but they're not obvious upfront. Basically, "essence" means characters who mainly play by aiming towards certain central win conditions or moves, whereas "fill" means sort of "throw the kitchen sink at 'em" characters who try to use smoke and mirrors to win the day. In the context of Melee, Ice Climbers are considered a "pure essence" character because wobbling/chain grabs are so fundamental to their play, while Falco is considered "all fill" at the highest levels of play because he really has to rely on his entire kit to win.
It's also worth nothing that just because a character is more "essence" or more "fill" doesn't mean they're only good at one or the other. Fox can do well in both (which is probably why he's arguably the best character there), but he's simply even better at "fill" stuff.
With that in mind, I made a quick chart for how I think characters fall in Ultimate. Characters are roughly in order, kinda?
Due to fundamental differences in the games, I think there's a higher percentage of "essence" characters in Ultimate than Melee, but I also am not that great a player, and my knowledge of every single character is limited, so take this whole chart with a grain of salt.
More than anything, framing characters along this spectrum has helped me think about why certain characters might appeal to certain types of players (regardless of competitive viability), as well as how characters may have changed in the transition between games. For example, I consider Mewtwo to be a "mostly fill" character in Ultimate because while it has certain kill confirms and reliably attacks (Shadow Ball), I feel like Mewtwo more often than not has to focus on trying to slowly build its wins using a variety of tools. However, I think Smash 4 Mewtwo is more of a "mostly essence" kind of character because of the stronger down tilt, the footstool disable, and the air dodge into fair to quickly turn games around.
Feel free to disagree with all the placements, but I also think it's worth thinking of one's own mains in these terms. It's not a very formalized or structured approach, but at least for me, it's helping me see Smash in a different light.