One use-case scenario for 13 button controllers is a leverless controller that has one extra button for your left middle finger in an optional WASD layout.
The Haute42 M16 can also be a WASD controller. As for the M13 edition, it has three less buttons than the M16.
The T series of Haute42 controllers comes in 16 or 13 button versions to suit your fighting game preferences.
The G series of Haute42 controllers can come in 16, 13, or 12 button editions in order to cater to your needs.
The FightBox M3 is a three-in-one hitstick that lets you use it as a lever, leverless, or WASD controller—and it has premium Sanwa parts.
The SallyBox is a mini controller with a layout that allows you to use it as a leverless or WASD controller.
The Pinebox is a stickless controller that is made of pinewood and is also available in a Super Smash Bros layout.
KeyCade offers a multitude of fightstick variations, including this interesting specimen, the BBL UVP arcade controller, that you can order with custom artwork.
Revolution Sticks makes unique fightsticks ranging from a guitar-looking fightstick to a simpler yet still flashy fightstick: the REV14.