I was wondering if carpet installation is easier if doors are not installed and how substantial the difference it makes to install doors after carpet. I would imagine it would be easier but by how much?
I'll assume you're installing a door and jamb, if you aren't installing a jamb I'd hold off on the door until the carpet is installed so it's not in the way
If you're installing the jamb I would do it before the carpet so the jamb can rest on the ground. If it has a threshold you'll have to install it before the carpet. I'd remove the door from the jamb and set it aside until the carpet is finished.
The standard procedure is to install carpet after the doors and trim are installed. If you were installing vinyl or tile, you would do the same, but hold off on any quarter round trim until you're done.
The important consideration, particularly for pre-hung doors, is how high to install it above the subfloor. With vinyl, you'd only leave a 1/8 - 1/4" gap. But with carpeting, we use a 1/2" spacer under the door jamb and floor (the same is done for any other wall trim and the floor). Just check the thickness of any flooring you're installing and adjust so you can run it right under the jamb and trim. The carpet installers will run right up to and under the trim for a seamless look.
If you are installing a pre-hung door and only one side is carpeting, then it's easiest to cut off a bit of the bottom of the door before you install it. After the fact, you can also use an undercut saws to adjust the trim height.
If the hinges have loose pins as is typical, it doesn't really matter because the doors can be removed easily. In this case other issues are likely more important for deciding the order.
Adding to pri0ritize excellent answer, it's much easier to shave off the bottom of a wooden door than to mow the carpet. :)