Originally this post was a complaint made by me, but after witnessing a few hours of gameplay, it remains unchanged. I was a complete muppet to think otherwise, please accept my apology.
I know 343i has tweaked somethings, but because they used the original coding the game including difficulty would play almost identically to the original. I played Halo:CE a couple weeks ago in prep for this, and at least IMO you do run slower, but the difficulty and damage dealt are the exact same as original. Not hating here, but is it a possibility that because of playing so much Halo over the years-CE, 2, 3, and Reach-you have just gotten better? I know it seems obvious but think about it, with as much time as many of us have played games of the Halo franchise, skill would have to go up. Again these are my opinions, and it is my wish not to offend anyone while stating my honest opinion
I imagine the increased FoV in CEA makes it appear as if you’re running slower. As for the other stuff, I dun know.
I guess it makes sense about getting better over these years, but the fall damage doesn’t seem right at all.
Try jumping off a 20ft cliff and you are guaranteed to lose all of your shield, maybe take a bit of health damage. I could have sworn that it never happened in CE though. I could be wrong though.
Nothing that you described has been changed. The game runs on the unaltered original code. As for appearing to move slower, it’s because the increased field of vision makes it seem that way. You are still moving at the same speed. And, don’t yoou think that maybe you’ve just got better at Halo, and so it doesn’t appear as hard?
And the Grunts are awesome. 
EDIT: About the cliff thing. I’m pretty sure you are able to crouch to avoid taking damage. I done it jumping out of the security building onto the beach on Silent Cartographer.
i just don’t like how the weapon ammunition is set up. you can’t see how many bullets you actually have. you can only see FULL clips.
also the co-op Bro Checkpoint Drag is sorta annoying because in some areas it’s very small. so sudden quick jerks or yanks happen even when you are right next to the other player, which can be annoying when running from the Flood.
> The biggest problem I seem to have encountered thus far is Legendary. Seriously, why is Legendary so much easier than it was in CE, this can’t be right. Those Red Elites (Major/Officers) were the bane of my existence in CE, but in this, they are a joke. On PoA, that mission would take hours on end to do, but in CEA, it only took me just below a hour to complete. I’m sorry, but Legendary is a joke.
Have you, for once, considered that in the intervening years between when you last played legendary and now you’ve become a better player? No, of course not because a 1:1 copy in technical fact must have been modified in ways that 343 specifically stated they would NEVER DO (namely, in gameplay and in AI.)
Even when it comes to something in your credit, you must still blame something else. 
I just (Two hours ago) blasted through PoA on Legendary in 6 minutes. Got half way through “Halo” in 15. I used to die like crazy and take hours to do this stuff. It does see, really easy for some reason.
Perhaps the smoother analogue sticks of the 360 controller play a role in the difficulty issue. I can see how that would make it easier to aim, and therefore easier to hit your targets more accurately.