The Games & More Custom menu is almost the same as the Smash Run Custom option minus the "Powers" option. Also, this is where you can only create your first Mii Fighter. For more details about Equipment and Specials, please refer to the link provided above.
There are three Mii Fighter classes that you can create:
Like the characters in the game rosters, you can modify their equipment, skills, and Powers. In addition, you can modify their Headgear and Outfit. Mii gear are rare drops in Smash Run and other non-Smash modes. Keep playing and you'll eventually unlock more customization options for your Mii Fighter.
You can create your own Mii Fighter by using saved Miis in your 3DS. If you don't have other Miis, you can use the default "guest" Miis on the left side of the Mii selection screen. Should you want to create your own Mii to use it as a template for your Mii fighter, you need to do it outside the game, in the 3DS's main menu.
Custom Characters
You can have up to 10 different Custom versions for each of the available characters in the game roster. In this menu, you can name each of the custom versions to differentiate them from each other.