Sounds to me like a test question at an integrity course. If you've decided you like the lens they sent, contact the dealer, tell them about their mistake and offer to pay the additional cost for the lens. If you decide you don't want to pay the difference or really wanted the f/4 lens, then send it back. The unacceptable option, IMO, is keeping the costlier lens and saying nothing. Regarding the pure question of the f/2.8 or the f/4 lens, I've never shot with the f/4 lens, but I do have the 70-200 f/2.8. It is a fantastic lens that I would not consider giving up.
"Nothing can be recognized without light and shade. It is only through the eye, the window of the soul, that we can truly understand the complex workings of nature." - Leonardo da Vinci