I use chrome for everything and occasionally have used Internet Explorer (or Edge) only to play MajCom games when (if) Chrome starts glitching. Lately Chrome has worked just fine. Not perfect, but pretty good.
Since the dawn of the Flash restrictions Chrome seems to work best. It will load the maps when I unlock the flash block but often I will have to reload numerous times to get the armies to stay there. I used to use Firefox (my preferred browser) and it works initially on MC but then will crash my computer with a grey screen of death.
I for one am looking forward to the completion of the HTML5 project