You are better of just watching gsmarenas videos and looking at their reviews for the X/S and GS 3 to see the differences and you will have to play with both yourself to see which one you prefer.
Basically (IMO), sense is a lot nicer looking and has a much better unified feeling for widgets and sense apps etc. it has a lot of functionality, the biggest advantage of sense over touchwiz is in the UI/colour scheme, camera area and gallery, the camera has a much nicer UI, very minimal but at the same time very functional and the gallery is feature full in regards to editing features, you can also see my review of the One S (below in sig) where I have taken screenshots of the most important areas for sense and talked about it (will be the same for the X as well). The colour scheme is much nicer as well (although I would prefer a black layout for the menus etc. rather than white)
I hated every sense version before, but love this new one, originally I would have replaced every app with 3rd party ones, however, I haven't

Mostly half sense and half 3rd party apps.
Touchwiz is considered to be lighter and better optimized* It has a lot of features as well and in the new touchwiz a **** load of gesture based stuff, however, you can pretty much get all these unique features of touchwiz (apart from gesture features) i.e. smart stay, touchwiz launcher with widgets, S-voice on any other mobile now (without having to root) and I am sure with time will see the rest soon.....IMO the colour scheme is awful, too "kiddish" and "cartoonish" looking and still seems to be disorganised, but it is smoother overall, I think this is just down to the animations used though.
* I thought touchwiz would have been lighter and better optimized as well, however, after seeing the GS 3 S4 dual core krait version compared to the XL/S, now I don't think it is (I know the S hasn't got the same res. as the GS 3 but the XL does and it still beats the GS 3):
http://www.anandtech.com/show/6022/samsung-galaxy-s-iii-review-att-and-tmobile-usa-variants/4