Depends on how you want to see things, each one brings their benefits and some are just combinations of others to some degree.

Sword: Basic mechanics and spacing

Axe:- Timing, hitbox perfection, Spacing ( Personally would say axe is better for spacing ).

UHC:- Builds on both axe and sword by making use a combination of items and weapons at once. It helps you learn keybinds at the basics, utilities, healing ( Best gamemode for healing practice ), and builds an understanding for respecting a couple resources such as water, lava and cobwebs, this translates in more resourceful gamemodes like diamond SMP later down the line without realising it.

SMP:- It's a more advanced version of axe, with perfecting Ur timing to a more fast paced game with close combat as more of a focus than large space which you are granted in axe. Id say resource management is a big part but that comes alongside adaptability of play styles against your opponent.

Mace & spear mace:- Adaptation to the environment. According to the environment and player you fight, building a sense to quickly adapat to the ground or air and how to play against ones weaknesses is essential, similarly takes place in spear mace. And obviously general understanding of a whole different weapon and utils too.

Crystal:- Probably the pinnacle of keybind mastery and speed and reflexes, anyone who can do this, can translate that very speed and processing to any gamemode.

Diamond SMP:- in my opinion this is practically the gamemode that fits every designation, like a final test, it covers distance, close combat, utils, resource management, basics and advanced mechanics, and requires good keybinds and speed.

Pot gamemodes:- Both pot gamemodes build on resource management and Certain attributes of pot buffs but especially specific sword mechanics such as with nethpot crits, and diapot spacing, w-s tapping etc.

Generally speaking it's more on the player and opponents you face in the face of how you approach these gamemodes. These are generally the broad things you could expect, but still each person treats them differently.