Yes, those are the three urls I've used as an example, although I did tests on a lot more.
http://norilskfilm.com/ - the then and now screen
http://sonsofgallipoli.com - chapters screen
http://karimrashid.com/ - main screen slider, if you scroll on the page I remember there were missing frames too
All websites are run on chrome, its the main browser I use because their developer tools are way better than any others. On safari some websites were smoother and others even more jumpy. Anyhow the performance on the Macbook Air was superior in all browsers.
I wanted to give these a fair test, so I tried it on my PC first (custom built - intel i7 2600k 3.4 GHz cpu, 16 GB DDR3 (1600 MHz) RAM, Windows 10 64 bit loaded onto a 256 GB Samsung EVO SSD with 2 factory overclocked Nvidia 970's in SLI): On the PC I used Chrome on a display of 1440p. It did't "chop", but the animations weren't super smooth on any of the sites. To me, it felt like the animations were 30 fps or perhaps less, sometimes more, giving it a little bit of a jerky feeling.
Then I tried the sites on my custom iMac (5k with the 4GHz skylake cpu, 8 GB of RAM (adding more eventually), 256 GB SSD and AMD m395x dGPU): For this I tried it on Safari as it's the only browser I have installed currently, at 5k. I found the performance to be exactly the same regarding animations, and if anything, I found the sites loaded a little faster which may be due to the better wifi capabilities on my iMac vs the one in my PC.
So I honestly found no difference at all. Not sure if that differs with the other iMac cards though I would strongly doubt it. My hunch is that maybe all the code/assets were cached on your other computers giving for a smoother look.
That said, I'm not blindingly defending the iMac either, that I also just dropped 4k on. It has it's issues too. While I think the graphics chip is "okay", and it performed better than I thought it would (thanks to all the negativity in posts), it basically performs a little better than my brothers Alienware laptop with the Nvidia 880m he got last year. For a 5k screen, I'm with everyone else in saying that I wish it was at least a Nvidia 980m inside, or would even prefer an official Apple brand external GPU enclosure for a beefier card - it would keep the heat outside the system, and would be optional for only those who want it, keeping the noise to a minimum for everyone else. My biggest issue though is heat. I am very uncomfortable that running any modern games, despite how well they run, drives my gpu up to 101 degrees at a constant rate, and the cpu depending on application under stress hits 89 to 101 as well. That said, those temps are apparently within spec, the system is extremely snappy, has great performance, and a phenomenal screen which is absolutely amazing for design work.
With that said, here's my opinion on the websites that nobody asked for
My thoughts on the websites are this: The first 2 were very neat in concept - I can really appreciate how they were brought to life, but I quickly became annoyed with navigating them, which is how many often feel after the initial "that's cool" feeling wears off. Navigation on these 2 sites I found frustrating. There is a lot to be said for familiarity - people expect the menu to be at the top or in a column in the left, the social media buttons/log in/etc to be in the top right, the main points to be "above the fold" i.e.: seen before you start scrolling because only 20% of your visitors ever scroll down. The third site was the best example mixing flashy design and navigation, but I still found pages by scrolling that were not in the main menu - "about", and because each subsection was basically on a different page, and I didn't have any scroll bars, I only found them by accidentally scrolling.
That said, I think there is a place for those kinds of websites too. Webpages for brands, whether that's bands, special upcoming events, products or whatever where the information is basically static - as in, not really going to be updating on a regular basis, just for info and presence, then these flashy kinds of websites are probably the best kinds of sites to do. It helps differentiate the brand and sticks in your mind. But if it's a site that has constant new content, whether it's news, articles, pics, video, whatever, those kinds of sites should never be used. When someone is looking for something, they want it instantly, and they expect to land on a site where they can quickly and easily navigate to what they're looking for. If that don't happen, they're gonna back button out of there to the next entry on the search page. As a designer I can appreciate that kind of artistry, but when I'm looking for info, I have no time for it, and that's the way most people are.