Whether it has one "gun" or three "guns", all color crts have three cathodes. The use of the word "gun" has become confused. One gun may be three guns connected together and thus defined as "one" instead of three. The important thing is that three color emitters (cathodes) are always used for color monitors in the current state of color technology. Thus diamondtrons and trinitrons would have the same type of convergence issues or not. I suspect that arrangement of the cathodes, if different between trinitron and diamondtron, could technically could impact the convergence and focus of each color. For instance, if each cathode is spread far apart, then the angle it which each hits the screen will be different and may result in incompletely overlapping color areas that is seen as convergence errors. With smaller differences, the angle difference diminishes. I don't know, but doubt that this is a significant issue between trinitron and diamondtron guns. The significant issue may be, as Goshark said, how well the convergence is aligned manually rather than the type of gun used.
I've noticed bad convergence errors in some genuine sony monitors, but more important I've noticed ghosting (different from convergence) as a recurring theme in sony monitors.
Quality is better than name brand, even regarding beloved AMD.