F-22 vs F-14? They were even tried one vs the other?

Since the Iranian Tomcats are still alive, why not? I don’t know if this question was already posed (AFAIK, no), but yet, i think it would worth some attention.

Two different super-fighters, even sharing some years in service in the USA (2005-07 or so).

The long range Phoenix/AWG-9/APG-71, put against the stealth but less armed F-22 (AMRAAM). The VG vs the hipermanouvrability. The speed vs supercruise.

I am pretty sure that USAF and USN made some DACT with those super fighters, especially F-14Ds, also because the IRIAF still has some F-14s active (and not forget about Su-27/30 and even MiG-31s).

So: who would win? Could the F-14 detect the F-22 and fire before the F-22 could fire at the F-14? Could the VG offset the F-22 advantages? I read nothing about, but it would be interesting.