Arcade sticks are good for fighting games such as Street Fighter 6, Guilty Gear Strive, Mortal Kombat 1, and Tekken 8. Fighting games usually require intricate directional movements and rapid buttons presses. You can accomplish such actions more easily with an arcade stick that has a tall joystick with big buttons laid out conveniently.
Since controllers have shoulder buttons, it can be awkward to do a combo with a combination of face buttons and shoulder buttons. Arcade sticks, however, usually have all face buttons, and the other buttons are often secondary buttons for pausing the game and so on.
Admittedly, games like Mortal Kombat may be better suited for controllers and not arcade sticks, but generally speaking, arcade sticks work fantastically for fighting games. Of course, they can work for other types of games as well, but make sure they do not require two analog sticks.
Most Street Fighter and Guilty Gear players use an arcade stick with a Japanese ball-top joystick, and many Tekken players, especially South Koreans, prefer to play with a Korean bat-top joystick. The Hori Fighting Stick α picked up in popularity yet again when Tekken 8 was released: