To my knowledge, the main difference between takeown and icacls (Integrity Control Access Control LiSt) is that icacls is a more general administration tool that among other things can be used by an administrator to grant ownership of a file or directory to a specified user. Whereas takeown is a more specialized utility that does only that one specific thing, specifically for the user running the command.
Both must be run by an administrator, and both commands shuld do the same thing if "User" is your username. The /t option for icacls is equivalent to the /r option for takeown (recursively grant ownership in subdirectories).
So both commands with those options should be basically the same.