I’ve done my own tests in 720p and never been impressed by any differences, so I currently create most of my work in 4k, airdrop or Dropbox to my phone and post straight to IG.
One thing I have noticed, is that if your shot is longer than, I think 10 seconds, you get a timecode showing in the top right hand corner of the cinemagraph. I never noticed until someone asked me how I got rid of it, and I realised that longer cinemagraphs show the timecode.
Another thing that’s worth considering, is cropping for quality.
Without a doubt, 16x9 shots look far worse than square, 3x2, 2x3 and 4x5. It’s important to crop for the shot, so while I prefer everything to be 4x5 vertical for quality’s sake, sometimes your shot loses some of the composition and story if you narrow it down too much, so going square or another format works better.
But if quality is all you’re concerned about, I don’t think anything beats 4x5 vertical.
As @mrjonkane mentioned, though, Vero is absolutely the place to be if you’re really trying to chase good quality. The CTO has a VFX background and kept quality a high priority for them, so any crop you post looks great. Sadly, if you turn your phone or click on the file to go full screen, you don’t have auto-loop, so you’ll have to make a longer cinemagraph for Vero, to accommodate anyone going full screen. But the fact that you can go to a larger view is awesome too.
I think many of us who publish on IG feel our work and audiences lose out because the screens are so tiny and people miss details and stuff we put such hard work into.
Good news though… Vero is working on an iPad version too! So that opens a whole new world of having an online portfolio with you.