I agree with your analysis and in my experience your points can all be found in the differences between Halo:CE and 2. The first Halo offers more in terms of all three of your points: The game environment is generally larger and there are more areas to explore (or at least, nooks and crannies if not full blown sections), There's a little non-linearity in certain sections, though not massively so you do get to do a few minor things (like getting 3 lots of marines air-lifted out) in a different order but also in terms of how you "attack" some of the larger scale battles (get a tank, or a warthog, or snipe) and this leads into the final point, there are entire sections of the game (mainly ones involving the flood) that you can charge through at high speed, or take your time to kill as many as possible. The former is more efficient but leads to the feeling that you've missed out.
Even though these three areas (and they do bleed into each other) aren't massively fleshed out in Halo:CE, when you play Halo 2, which feels more firmly on rails, and confines you to a number of set piece battles interspaced between sitting on an elevator/gondola/light-beam-thing/kayak and waiting you realize just what it is you are missing out on.
I think somewhere in my rambling was the point that it's sometimes more subtle than you realize, and that a game doesnt need to be GTA "open" to feel open.