I've never ever had a rope halter tied in the first manner get so tight I couldn't get it off. Supes has sat back and thrown himself down, gotten up, sat back again... halter just came right off when I pushed that rope back through the knot. Sarge threw his silly butt completely down at a rodeo, in wet grass, while tied tot he stock trailer... and I had to cut the lead rope because someone else (not me) had tied him without using a slip knot at the trailer end. The halter itself still untied easily. That one horse daughter had, Jackie Brown... sat back hard enough she broke hers... Sally as well... both of those two goofy heifers knew how to pop them off and I'm pretty sure each one destroyed two or three rope halters in the few months we had them.
I've used rope halters just like the one in the video, and I've used the mule tape types... never a problem getting them undone.
The second option looks like more of a headache - this guy himself has to take a few extra seconds to split the two ropes that go over the poll to tie it, and then untie it, but he could just be doing it slow for the purpose of instruction, IDK. I mean... if it works that way, go for it. But Option 1 has never given me a bit of grief, even when the horse has.
"We are here to laugh at the odds and live our lives so well that death will tremble to take us."