You will have to use % and px as units of measurement for pages and other elements like divs and other related elements.
You need to use % for responsive layouts. But still, using px units will be required for some cases.
It is better to use em for texts. Usually 1 em is 16px unless the developer or user specifies a default font size.'
Developer can change this default value from 16px to anything he/she wants by setting the font-size for body selector in the CSS.
Users can change the default browser font-size in the browser setting.
So if you use em for fonts, it will be good for the users. They can increase the font size very easily without zooming into the page.