Most DOS games have a resolution of 320x200, some 640x480 and then there are a few ones with more weird/exotic resolutions.

Only the native resolution taken times a whole number, i.e. 2x, 3x, 5x, will yield pixel perfect results.

So on a 320x200 game it would be these resolutions:
320x200 \ 640x400 \ 1280x800 \ 1600x1000 (FullHD) \ 1920x1200 \ 2240x1400 (2k) \ 2560x1600 \ 3200x2000 \ 3840x2400 (4k) \ 4480x2800 (5k)

Dunno how DOSBox-X handles this, but on the regular DOSBox to have these centered on your screen with black bars around, you will have to add the horizontal number of your monitors native resolution, for example:
Your monitor is FullHD 1920x1080, then the ideal max resolution for the game would be 1600x1000, therefore on the fullscreen setting you'd type 1920x1000.

In your case it should be 1440x800, if the game has 320x200 as base native resolution.

All aspect=true does is change the game from a 16:10 (if 320x200) to a 4:3 ratio, but that results in rectangular pixels instead of perfectly square pixels.
There is lots of different opinions wheter or not to play with the correct aspect ratio. I personally say, if you have a 16:9 monitor simply stay with the 16:10 aspect=false ratio for 320x200px games.

BardBun wrote on 2021-05-06, 18:02:

Most DOS games have a resolution of 320x200, some 640x480 and then there are a few ones with more weird/exotic resolutions. […]
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Most DOS games have a resolution of 320x200, some 640x480 and then there are a few ones with more weird/exotic resolutions.

Only the native resolution taken times a whole number, i.e. 2x, 3x, 5x, will yield pixel perfect results.

So on a 320x200 game it would be these resolutions:
320x200 \ 640x400 \ 1280x800 \ 1600x1000 (FullHD) \ 1920x1200 \ 2240x1400 (2k) \ 2560x1600 \ 3200x2000 \ 3840x2400 (4k) \ 4480x2800 (5k)

Dunno how DOSBox-X handles this, but on the regular DOSBox to have these centered on your screen with black bars around, you will have to add the horizontal number of your monitors native resolution, for example:
Your monitor is FullHD 1920x1080, then the ideal max resolution for the game would be 1600x1000, therefore on the fullscreen setting you'd type 1920x1000.

In your case it should be 1440x800, if the game has 320x200 as base native resolution.

All aspect=true does is change the game from a 16:10 (if 320x200) to a 4:3 ratio, but that results in rectangular pixels instead of perfectly square pixels.
There is lots of different opinions wheter or not to play with the correct aspect ratio. I personally say, if you have a 16:9 monitor simply stay with the 16:10 aspect=false ratio for 320x200px games.

Really appreciate this wonderful and informative reply!

smonk wrote on 2021-05-05, 16:31:

Which one is the correct setting for the correct output?

I'll try to answer under assumption 'setting' is aspect ratio, and 'output' is desktop/native res.
Will also assume the 'correct' is full screen and PP display enlargement.

First I'm also unfamiliar how DB-X works but as far I understood, in vanilla, difference between desktop and native resolution output is the former works correctly on all monitors. It's surprising to see it render @ 768 in your case. So the correct is 'desktop' unless it doesn't work. In that case native replicates the job but you'll have to manually edit the numbers if you change to a monitor using different native res.

Correct aspect ratio is more trickier because today pixels are squares whereas before they were tall rectangles. Most games were designed with that in mind so displaying them on monitors of today produces some visual artifacts. You can visit this link 320x200 : The Resolution of Choice for the IBM PC and click Elite images down bellow to easily illustrate the problem (you can skip the color part entirely). Putting 'true' will almost always produce 4:3 image ratio (with black bars on the sides to fill the screen) but some circular graphic in game will become oval shaped. 'False' will correct the circles but stretch out everything else, often as they should be. 'Correct' comes down to personal preference and to me is to have proper circles above anything else.

Pixel Perfect just enlarges the original image in a way BardBun described above. It's a rarity to be able to play PP and full screen at the same time with all 3 most common vert resolutions of the day: 200/240/480. You'd need a multiple of 1200p display. In your shoes I'd go with [Aspect=True] [1440x900] unless some ovals in da face rustle my feathers, then I'd change to False. Al least it'd be easier to aim at the fatties.