I don't think "Me quedó a la salida..." is correct. It should be "Quedé de (en) verlo a la salida" or "Quedó de verme..." or "Quedamos de vernos..." And yes, both are basically the same. I think the word "citar" is a bit more formal. Citar implies the other person told you the time and the place you're going to meet them regardless of your opinion, while quedar is more like an agreement. You can say "nos citamos..." to imply you both agreed to do it.

It is correct to say, "El decidió reunirse conmigo de la salida del cine.

Bueno la diferencia radica en el campo de aplicación, es decir. cita= place and time. quedar=agreement or arrangement