Depending on what it was filmed/recorded, absolutely. That special was definitely recorded in HD, so the image quality was great, even casting from my phone to my TV to watch it. Filmstock and video degrade with time and use, and in the very old b&w days some of it was still handcranked, so frame rates weren’t consistent, so things could appear jerky or oddly paced. Depending on who filmed the original footage, too, there was a framerate difference between the US and Europe, so conversion could sometimes make action look odd.
Also, I would guess, is that horse maintenance has changed sine the b&w days, too, so they’re getting things like joint supplements that would keep them performing better, longer.