I obtained the following:

$ time $(tee < infile > outfile)
real 0m14.721s
user 0m0.094s
sys 0m2.629s

$ time $(cat infile | tee > outfile)
real 0m8.931s
user 0m0.123s
sys 0m3.168

Is that difference just owing to redirection/piping, or is there something else going on here? Running them a second time gave the following:

$ time $(tee < infile > outfile)
real 0m11.558
user 0m0.113s
sys 0m2.691s

$ time $(cat infile | tee > outfile)
real 0m8.822s
user 0m0.120s
sys 0m3.125s

PS: Both infile and outfile were mp4 files, cached in ram; if that makes any difference.

Edit: I meant tee < infile > outfile and not tee < infile tee > outfile.

The examples are not the same as in the title.

For the question in the title.

The version with cat will be marginally slower.

For the question in the body

The first command, is writing two files. This is why is is slower.
The second is starting an extra process (cat), but this is a small slowdown compared to writing extra file.

The second run is faster, probably, because the read is cached.

Explenation

tee < infile tee > outfile is functionally equivalent, but faster than cat infile | tee tee > outfile, where as tee > outfile is not. The first two produce two file, the 3rd produces one, so will be faster.