I've been doing a little reading and here's my understanding of the downsides:

TIE Fighter 1998:
Horrible music; TIE Fighter Reconstructed will change this to reasonable but still non-dynamic music.
Enemy units with advanced concussion missiles they shouldn't have. (Isn't there a fix for this?)
Cutscenes in wrong aspect ratio.

TIE Fighter 1995:
Platforms and capital ships not firing. After reading several threads, there doesn't seem to be any very definitive fix for this - the best one can do is compromise between it and FPS drops.
Arguably-worse graphics. (I'm not saying everyone has to, but I think I prefer the TIE 98 graphics).

Any advice?

It may just be the nostalgia for me, but the way the music changes in the old version always gave it an epic feel. I keep going back to the older one whenever I feel the need to destroy some Rebel scum. The graphics are probably the hardest thing to get past on the older version though.

Ah the building of the battle music as you approach your targets :)

I think I'm more fussed about gameplay problems than either music or graphics. If there was a definitive fix for the advanced concussions in TIE 98, or for capital ship fire in TIE 95 (rather than "fiddle with DOSBOX and hope"), I'd go for the version with that fix.

In either case, a great game to play.

Have you tried using one of the old mission editors to switch out the advanced concussion missiles to regular concussion missiles for some of the enemies? There still a website around that hosts the editors here. Not sure if it works with the 98 version though.

I remember using the Workshop Editor back in the day just to see what I could throw in. (TFW2B4.ZIP).

http://sco.emperorshammer.org/sco/SCO/sco.tiranto.com/sco/files/tie/misedit.html

The workshop editor works on the '98 mission files. (That said, does TIE 98 interpret what it's given in the same way?)

However, I looked a bit further. The mission I find people complaining about is Battle 1, Mission 5; the editor shows A-Wing Blue (and Red, on Hard difficulty) with standard concussions; Yellow and Gold (launched if the cruiser is attacked) with advanced concussions.

If I play this mission in TIE 98, Blue and Red still launch standard concussions. If I play it in TIE 95, Yellow and Gold still launch advanced concussions.

This does leave me wondering if this bug definitely exists. Can anyone name a mission which actually behaves differently?

(Oh, but TIE '98 has another problem: ISDs not firing. And there's a fix for that, but it doesn't work with the Reconstructed music. Sigh.)