How does the 360 version on One compare to the fully remastered/ported version?

Sorry for the late response!

Digital Foundry has a video covering the differences here:

TL;DR: Framerate is more stable on Xbox One and picture quality is improved. Not sure about loading times. Can't really say if anything would change from a speedrunning context since I don't own either Xbox version, but I imagine the One version would be better simply due to performance upgrades.