Before you get started, it's good to note that you don't need Redux to play this. You could use the free version on Steam. Both versions work the same, you just get the expansions (Which you can download online) from Redux.
The original release of Shadow Warrior is on Steam for free here

Go here to download Eduke32[dukeworld.com] (It comes with VoidSW as of the writing of this video. This may change at some point).

Extract the file somewhere on your hard drive

Launch VoidSW within the folder and select the expansion you want to play (The expansions won't show if all you has is the '97 release downloaded. I'd advise not downloading both the original and rerelease of Shadow Warrior because that may cause bugs with VoidSW, I'm not sure)

These pictures are taken on No Pain No Gain

VoidSW
Redux (Notice the washed out colour and the lack of shadows. The sword sprite is tweaked for widescreen in redux though. There is a fix for that for VoidSW)

VoidSW
Redux

VoidSW
Redux

This next one is a bit hard to see the difference because I was being shot in VoidSW unlike Redux (It's really hard to take comparison pics because I don't know how to use cheats)
VoidSW
Redux (Notice again the lack of shadows)

Some effects bugged in Redux like blood pools. They appears slightly below a floor, which in most cases makes them just not show up at all.
VoidSW
Redux

In the original Shadow Warrior and VoidSW, blood pools showed up for some if not all kills.
VoidSW
Redux

Another problem that I cannot really take a picture of is the mouse aiming. Mouse aiming is like a D-pad being emulated by a mouse in Redux, while in VoidSW, it's just like any other game. Normal aiming. Nothing more to it.

Have fun or else

Also I'm a ♥♥♥♥♥♥♥♥ idiot and I don't know how to properly embed pictures I'll try to fix that soon folks yikes ._.