You would be surprised Big! The Russians copied the AIM-54A Phoenix and call it the AA-9 Amos (R-33) and arm their MiG-31 with 4 of them. The R-37 was to replace these and up carriage to 6, but as of this date I can find no evidence they were ever produced (R-37 is an enhanced R-33, to the level of our AIM-54C Phoenix). The MiG-31 actually has superior radar to the F-14s, as it is digital fxed scanned array, however its reliability is in question.
The MiG-31, while better stressed for maneuver then the MiG-25, can not dogfight with a Tomcat, though it does carry a rotary cannon of similiar capability to the M-61 Vulcan...
They even look alike..
AIM-54 Phoenix Pic.

R-33 Amos Pic.

Carriage is even close to the Tomcat with all R-33 missiles carried on the belly...

Four R-33 (NATO AA-9 'Amos) semi-active radar homing long-range AAMs in pairs on AKU ejector pylons under fuselage. R-33s are semi-recessed in fuselage.
Two R-40T (AA-6 'Acrid') medium-range IR AAMs on inner underwing pylons.
Four IR R-60 (K-60, AA-8 'Aphip') AAMs on outer underwing pylons in pairs.
GSh-6-23M six barrel Gatling-type 23 mm gun inside fairing on starboard side of lower fuselage, adjacent main landing gear with 260 linkless rounds.