I will talk about two joysticks:
First the best one ever made, with the best control (that's what it's made for) is the megadrive Quickshot Chimera 3, that I use in my miggy:
You control all movements with two fingers, and you use the right hand for the buttons. It's insuperable (IMHO).
Just an observation: How are all of the joysticks now, Playstation, XBox...? You have them in your hands, you control movements with your left hand (one or two fingers) and the buttons with the right hand (some with the left one, sometimes loosing control). If there were less buttons (for an Amiga, for example) and without vibration, you would have them exactly like mine that I bought in the 90's... and what about using a button just like a gun (can you imagine it?) and having a firm grip in your right hand?. Ah, and it's got Autofire too.
And the second, which I don't like very much is this:
If you need a big button, it has "The BUTTON". Watch a video to see how to use it:
http://www.youtube.com/watch?v=FT4YbO_1mvA