Since I couldn't really find any other places explaining this (not even other websites with forum posts from the early 00s that are still somehow active), nor any comparison screenshots, I am just wondering: what does the "compression" graphical option go in the Hitman games? Hitman 1 has "texture compression" and "palette compression," and both Hitman 2 and Contracts have "DXT Compression." I even attempted to see if I could tell any difference between "on" and "off" in Hitman 1 by loading up the first proper level and looking around the area with the Buddha statue, but I can't say I was able to notice any difference.

I suppose my biggest concern is if it's better to have these options "on" or "off" in order to have the best visual quality.

Generally, in games, texture compression is introducing minor loss in quality of textures to allow for better performance: https://en.wikipedia.org/wiki/Texture_compression

So, you'd turn it off unless you're looking to tweak performance. For games in general. But games have a real hard time explaining themselves, so I can't say for sure in your specific use case. BUT, if you can't tell the difference, why worry?

This setting can be confusing, in older games it usually means an IMPROVEMENT of texture quality.

Without compression, only poor textures can be used. But with compression, higher quality textures can be used.

Some games explain this (Medal of Honour), but mostly it's confusing. The visual difference should be very obvious though, so it's easy to try it out :)

There is absolutely no visual difference in Hitman with compression on/off

Could be anything, I only explained that texture compression options in old games means "high resolution textures".