Fun is a very hard thing to pin down -- because it's composed of "fuzzy" sorts of concepts like challenge, choice, reward, punishment, variety, novelty, emergence, pace, flow, feel, and so much more.
Take a simple jump in a platformer, for instance. You can have a nice sort of parabolic jump that mimics gravity, or you can a linear up-down jump that doesn't. Both of these things can otherwise have the same properties (like max height / max distance) and so they perform in basically the same way as far as level design possibilities go. But the parabolic jump just feels nicer -- it has weight and gravity -- and that makes it fun; the linear jump feels cheap -- and that makes it boring. That's not to say that realistic physics are fun -- Super Meat Boy completely throws off realism to pursue "feel" 110% which its creators have spoken about several times -- even in the original Super Mario Brothers for the NES, Mario and Luigi's jump arc is not physically realistic (they can jump several times their height), but it doesn't even follow a single parabolic motion -- the parabolic arc they follow on the initial rising half of the jump is different (it "floats" more) than the falling half -- which gives their jump, and indeed the entire series, a very distinct feel to them.
That's just a single concrete example, but its illustrative of the fact that mechanical equivalence rarely implies that there's a similar amount of fun to be had.
There are a wealth of videos on youtube where games, design elements, and game mechanics are broken down in very critical and analytical ways. I recall being very impressed with one video which broke down how the camera tracking in Super Mario Bros evolved throughout its 2D incarnations, which I wish I could find and link to right now. I'd be remiss to not plug my coworker's excellent game design channel, Game Design Wit, but there are a lot of content creators doing these kinds of videos.
Edit: Found it -- How Cameras in Side-Scrollers Work
