I played X-wing and Tie Fighter back in the dos days. I remember when I first got the GOG version that I couldn't get into it because the Cap ships never fired correctly due to issues with the emulation. The game could be smooth and easy (as the ships didn't fire much) or slower (than the original) and them firing "correctly". Has this issue been corrected or are there other dosbox forks like dosbox-x that might correct this issue?

The ships not firing is not an emulation bug, I've tested it myself on an old pc. It was just a myth some guys were spreading here. So there really isn't any way to fix it.

You are right that it's an inherent bug of the game's engine, but it's not exactly a "myth" that the emulated version shows the issue more frequently, simply because of the fact that a) it's easier to alter the CPU speed and inadvertedly trigger it than on a real hardware and b) being emulated, the SVGA version needs a little bit more horsepower than in a native environment, hence people do a) more often.

X-Wing doesn't usually show the problem simply because running in normal VGA resolution you can keep the cycles around 30.000 or something, and still have perfect performance, while TIE CD in SVGA needs to go to the "bug limit", more or less in the 60.000 mark, to be somewhat smooth but with working cap ships

I wonder if some of the other dosbox forks work. Maybe one of them can run it smoother at lower cycles.