They definitely blew that one: using footage that isn't suiting to the text
and the story.
The Shah has not "ordered" a fly-off: he requested the opportunity to fly
each plane AFTER the IIAF has already made its mind. The fly-off was offered
to him after all the briefings in Tehran, and because the Pentagon would not
let him fly the F-14 or F-15.
Iran, nevertheless, ordered F-5E/Fs already before it ordered the F-14s:
these were intended as interim solution unitl the decision about the YF-16
or YF-17 would be made.
Re. speed: the F-15 should have the official top speed some 200km/h higher
than the F-14.
If you're confused about the quality of the show in question, it's easy to
find out how well researcherd it is: have they maintained that the F-14 saw
no serious service within the IRIAF during the war agianst Iraq?
Iran-Iraq War in the Air, 1980-1988:
Iranian F-4 Phantom II Units in Combat: