MCC was allegedly an entirely fresh port by 343 without using either of the previously deficient PC ports. It is said the port/rewrite was a big part of 343 getting familiar enough with the engine(s), documenting what Bungie hadn't entirely documented and 343 hadn't pulled in as headcount in the messy divorce, and making the engine their own in the path to building Halo 5. In my experience that seems to track in that a lot of the "feel" changes from the original Xbox versions seem to me to align with how Halo 5 feels to me.
The mcc collection never felt right to me in terms of game feel.