I assume since you say “joystick” vs control or center stick you’re talking about flying large jets (Airbus) and not general aviation like a Piper Cub or a Cyrus? If you are talking GA no there really isn’t much difference at all, as Chris pointed out you’re generally flying the yolk one handed. BUT if you’re talking large jets, yes, in my humble opinion there’s a HUGE difference. The biggest difference is most yolks are either actually moving some wires or control service and even if they aren’t there’s some “synthetic” feel built in which gives the pilot feedback as to what the airplane is doing. The joystick is completely fly by wire (meaning you’re sending commands to a computer and the computer is moving the control services) and there’s zero feel or feedback. The sticks also autotrim so as soon as a control is moved the computer will “trim” the control surface to eliminate the need to hold any pressure. Inputs with the stick are incredible subtle and it’s very easy to over-control. It’s really a very different experience.
As to popularity it’s really a matter of what airplane the airline your flying uses, Airbus or Boeing.