diff while ignoring patterns within a line, but not the entire line

You can use temporary streams to avoid file creation and cleanup, syntax is following:

$ diff <(command with output) <(other command with output)

In your case:

diff <(cat f1 | sed -e's/^\[....-..-..\]//') <(cat f2 | sed -e's/^\[....-..-..\]//')

Hope this helps.