I have the X Chocks. I'd never seen the Quick Products chock before. I looked at the pictures and watched the video. Here are my thoughts based on never having the Quick Products item in my hands or using them, but using the X Chocks for months now.
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The Quick Products version needs to be adjusted by turning a nylock nut on a threaded rod, then the lever can lock in the up position with pressure on the tires. In situations where the vehicle might need to be released from the wheel chocks quickly, this could be a big plus. Flip the lever, and you're pretty much free to go at that point. Fast and easy for sure.
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In my experience with my trailer so far, no parking situation I have been in has put the wheels in exactly the same position as when I have removed the X Chocks. When I first got the X-Chocks, I would loosen them just enough to slip them out from between the tires, stow them, and be on my way. My thinking was that when I got to where I was going to install them again, they would just slip in and only need a few turns of the wrench. When I reached my destination and parked, I quickly noticed that there were times that the X Chock wouldn't slip between the tires to be installed, or needed to be adjusted wider to fit in the space. I have a couple of ideas for why this is, but haven't tried to figure it out. Uneven terrain is sure to be one reason. If I have to adjust my X Chocks as often as I do, I don't want any more complicated a system to make that adjustment. It seems to me the Quick Products chocks would be more difficult to adjust for my needs. If you only park on smooth level pads, the Quick Products item might be perfect for you.
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The Quick Products design adjustment range might be the real limiting factor. The slot that a pin sits in is only as long as it comes from the manufacturer. The X Chocks have a wide range of adjustment. Both designs may not be very strong at the outside range of their adjustment, but it appears to be easier to move the X Chocks between different vehicle if you would like to.
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The steel "pads" that contact the tire on the X Chock swivel on pins for good full contact with the tires. The contact areas of the Quick Products design don't seem to.
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I don't know where to buy the Quick Products item other than Amazon and direct. I can get X Chocks at Camping World and a few other places easily. If I lose or break an X Chock, I can easily and fairly quickly replace it. They cost more, yes, but in my opinion the X Chock is a better design for the task.
All of the above is only my opinion, worth less then the electrons you're using to view it.