The Pi 4 has a faster processor (1.5 GHz Quad-Core ARM-Cortex A72). I am wondering if it is now possible to watch HTML5 videos on a browser (for example YouTube) and with 1080p quality without lagging and sticking?
In this review, RPi 4 was able to play a 1080p30 Youtube video smoothly, but not 1080p60. There was observable screen tearing, but I'd expect the situation to improve in this regard as Raspbian is polished for RPi 4 support.
Note that there's also a method to offload the video playback from the browser to an external video player, which sometimes was the only option for smooth online playback on older RPi with their limited memory and slower CPUs. It will probably improve the playback on RPi 4 as well, but it may well be no longer necessary if Raspbian gets enough polishing to support a flawless in-browser playback.