scotsdezmond: I know the OP was regarding the Windows 1998 version, but if using a 360 pad with the 1994 DOS version, I can recommend replacing the dosbox exe with an alternate custom build. (I cannot attach the link myself, since this is my first post, but google "dosbox joystick deadzone" and choose the "Custom Dosbox | David Walters Development" link.)
This build includes a joystick deadzone parameter that can be placed in the dosbox.conf file. I installed this by replacing the included dosbox.exe in the Tie 94 install with the new version, and then added the deadzone parameter manually into the dosbox.conf file.
My 360 pad has a very sensitive left thumbstick, so I've set my deadzone value to 15, and it works much better - I don't get any drifting after sharp turns, but you can adjust this as YMMV.
flyinj: Good info, but I really can't go back to 320x200.
I know the feeling. I also have my original '95 Collectors CD set up this way in dosbox too, although I use it less frequently since it's a pain to put the CD in every time.
Another suggestion might be to try the Joy2Key setup by SavingContent, download the Tie95-win7.zip from this page:
http://www.savingcontent.com/2014/08/09/guide-play-x-wing-tie-fighter-series-on-windows-7-windows-8-windows-8-1-with-an-xbox-xb1-playstation-ps4-controller-flight-stick/5/.
Inside the zip file, there is another zip file called jtk374en.zip, extract this to a new directory and run the exe.
Select the Tie95 profile on the left, and then the 'Others' tab on the right. You can try adjusting the slider for Threshold for input: I've set mine at 20%. Then launch Tie98 via the GoG launcher as normal.
It's certainly playable but a bit twitchy at times. The other benefit of this method is that you can use the controller for navigating the screens inbetween battles, much like the original DOS version. I find it handy since my system is connected to my TV, and gaming from the couch is much easier with a controller.
