I used to be in the that boat, where I looked at screen shots and thought "Ah, that's not a big difference".
Now that I finally (After like 5 years!) got a new computer with some decent specs I can easily see the difference once everything is in motion and running crisp.
Oh, I can see the differences on a technical level. And I can even lay them out here in technical terms. I just wish not to get into a discussion/argument with people here as a) I don't have the time to spend on debating such things when I barely have time to play and b) most here aren't interested in learning as much as they are finding analyses, opinions, and members that support their stance in order to create group-think and popular opinion and to propagate it as fact.
I know there's a fair difference between the PC and console versions on a static technical level, but it's the dynamic side that makes the PC version pop with life to me personally.
I notice that with the lighting in many PC games now. Especially when I put some mods on Skyrim.
The first advantage that was instant, for me, was rez. Then, the individual advantages likfe textures (ex. fill rate, mip-mapping), use(s) of anti-aliasing, and FPS, and this is all before you get to the NVIDIA Control Panel (for GeForce users) or mods.
Whole other world that I was finally able to afford. :P
Edit: I see your edit about the controller. Since you're gaming on a laptop, it makes sense, but when you become a full desktop PC gamer, I can't stress enough how much the kb+m combo will make you re-think how you play games, in general! So intuitive and precise.