The reason you aren't getting what you want out of the command is because you are redirecting the error output from the wc command into time.out. NOT the error output from the time command.
What you need to do is this:
time (wc filename >wc.out) 2> time.out
That will redirect the output from the wc command into a file called wc.out and will redirect the standard error output of the time command to a file called time.out