Have a look around the forum. This very question ahas been posed many, many times and there is a huge amount of good information out there. If there is a specific mixer you want to compare to the S4 - that might trigger more of a response.
A hardware mixer will have much better build quality than the S4 including usable VU meters and plenty of inputs. You can of course easily mix from external sources without the need for a laptop.
Most 4 channel mixers will have their own FX too which you can use in addition to Traktor’s FX.
External Mixing has better quality but it’s portability is not as great as that of an S4. Keep in mind that with an external mixer and an x1 you will most probably have to use sync and you will not have access to faders. For me this is an issue because traktor’s sync capabilities are not always on point. Also if the sync is slightly off you will not have jog wheels to slightly adjust your mix. Also, if you get a good mixer and an x1 later down the road maybe you can add some cdjs to your set up. Just a thought. At the end of the dsay it’s your money, you’re the one using the equipment so just do as much research on the both types of systems and see what you prefer. I’d also suggest heading out to your local music store to check out what they have on display so you can get a feel for it.
Mixer and X1. I have a Nuo 2.0 and an X1. With a very lightly modified mapping, I can perform very easily; it also fits in a 10 inch mixer case with no problems. The reason I wouldn’t go for the s4: sooner or later you’ll want decks. When you want decks, be it CDJ or Vinyl, you’ll need a mixer. And if you go mixer+x1, VOILA you already have a mixer!
I think people have forgotten this for some reason. Nudging tracks that haven’t had their grids corrected yet into phase is a pretty easy task. And if you’re mixing externally how do you not have access to faders? Last I checked most (all) mixers have those .