I’m going to respond here bc I’ve just come out of some work meetings that pissed me off and have me fixated on the value of plain speaking. So if I seem like I’m dismissive I’m really not trying to be, but rather just influenced by my own context so keep that in mind.I have tried both ways and don't seem to notice any difference. Never noticed the strop to ever make my knives shaper, sometimes just duller if I'm not careful. I also know there is a science to it all and not one way will work for everyone but I'm interested in the science of it. If I understand the science I can build upon that. Like typically most people have better luck removing a burr edge leading but all the close ups show trailing can give a better edge. Both don't work for me except raising my angle to remove the burr then back sharpen to take out the micro bevel. Hearing others experiences helps learning also, maybe there's a different way I didn't think of trying. Or knowing the science I can come up with my own unique way
You will struggle to find a forum more interested in parsing the value of different sharpening and stropping techniques than this one. And @mengwong is probably one of the members most into analysing and responding from the perspective you’re chasing (imo only, and I hope that’s not offensive to either @mengwong or anyone else!)
But honestly you’re trying to get a ‘scientific’ answer to a question that isn’t actually scientific. There are so many different variables and implicit and explicit assumptions in asking “should I strop heel to toe or toe to heel” that there isn’t a simple ‘scientific’ answer that can guide you.
There are some awesome scientific resources, and the ones that @mengwong has linked are great and have had a big influence on my approach. But they’re very specific to a set of parameters, and they’re only one person’s evaluation. I still put a lot of stock in them, and it’s scientifically oriented, but that’s not “science”. Add in your own circumstances and approach and it quickly becomes even less applicable.
So when someone says just do some sharpening yourself and try it out it’s not to avoid the question, but actually to make it relevant to your context