Does HTML5 Canvas have trouble playing concurrent movie clips?

I am an avid but amateur Animate user.

I am trying to manually convert an AS3 project in HTML5 canvas.

I know that I need to:

1) Change code commands from AS3 to JS (No problem.  I only use 'stop" and click to go to frame label.)
2) Remove filters like bevel and drop shadow (It doesn't look as sophisticated but no problem) 

3) Avoid Motion Tweens and Shape Tweens (no problem, Classic Tweens will have to suffice.)

But I still have one problem. One the web, some phones and tablets play the project quite slowly - too slowly.  By contrast, desktops, laptops, and iPhones play it perfectly.  I'd like the project to play briskly and smoothly on all devices.  After some observation I have noticed that the phones and tablets that play it slowly seems to have trouble when 2 animations (concurrently playing movie clips) are running simultaneously on screen.  I never have this problem when the original AS3 project runs as Android and iPhone apps; it runs seamlessly no matter what device they play on.

My QUESTION:  Does HTML5 have more difficulty than AS3 playing concurrent movie clips? I am reluctant to remove all concurrently playing animations because that is a major aspect of the project- but I will go it to get the project to play smoothly on all devices

Thank you.