For desktop browser all modern browser uses Zoom functionality so we can use PX but if same site can be seen on mobile then would px not be good for zooming in mobile browsers.
PX is a fixed pixel size EM is relative to font size
So really, yes you should probably use EM for a lot more of web sites. It will let a user define how large they want there font and your site can scale around it.
However, most web-devs like the more specific PX as they can know exactly how things are displayed relative to each other.
But seeming as desktops and mobiles have such drastically differing resolutions, its probably just going to be easier to redesign your site for mobile browsing.