Street Fighter II seems to have buggy 2-button support. You are better off playing Super Street Fighter II AGA on your A1200 anyway, which as fitzsteve mentioned needs to be changed to 2-button controls in the options screen. How many other 2-button supported games have you tried?
A simple way to test if both buttons (B and C) work is to plug it into the mouse port and press the C button to see if the menu bar appears at the top of the screen. You can also download JoyTest from Aminet which can be used to test all joysticks and control pads -
http://aminet.net/package/util/misc/joytest_CPHave you tried these games you're testing both from floppy disk and through WHDLoad? Although it doesn't affect my A1200s, there seems to be a bug in WHDLoad preventing the second button from working in any games on my A600, but those same games when played from floppy disk allow me to use both buttons. I have tested my A600's ports with JoyTest and it works perfectly with 2-button and CD32 (7-button) controllers, as well as regular 1-button joysticks of course. So, there could be a bug, or perhaps a setting we're missing in WHDLoad that prevents installed games from using the second button on some systems.
Another problem sometimes encountered with 2-button (3-6-button Sega) controllers is when they are used with a game that expects a CD32 controller. Pressing the second button (C) sends the same signal as pressing ALL the buttons at once, including the Play button, which will cause the game to pause.
So my advice is to try more games, try JoyTest, try the same game from both WHDLoad and from floppy, and try a game that runs from the hard drive but doesn't need WHDLoad, like this little game demo I made a couple of years ago which has the option to choose between joystick and control pad -
http://aminet.net/package/game/demo/HalloweenNightmareDemoI hope you find out what's causing your second button not to work. Good luck!
