Media Center explicitly (meaning, on purpose) does not have an option like iTunes. Files are always imported in-place (meaning, without moving them or creating copies). MC will only move, copy, or rename your files with explicit user permission (meaning, you initiate it yourself).
However...
It does have a very powerful system for moving and copying files. To use it, you simply select some imported files (this can be just one, or many) and do Tools > Library Tools > Rename, Move, and Copy Files.
This tool can move or copy files to the directories and disks of your choosing and rename them to create new filenames and directories based on the tags in the files. This is much like how iTunes "automatically moves and renames" your files, except that you get to control when, how, and where they are moved and what filenames they end up with. If you want some files to be moved with one set of rules, and other files to be moved with another set of rules, you can make presets in the tool and recall them later to use them again and again.