Yak-38 or Yak-144 vs Harrier
Assuming it was a Harrier FRS1, (Sea Harrier, the most likely opponent as both were carrier based in the main), then I think the Sea Harrier would have the edge. Mostly down to the pilots, although I believe the Sea Harrier had better radar, (happy to accept correction).
If this was the 1980's then we're also back to the R-60 Vs AIM 9L question too.
Guns wise, the Sea Harrier had the 2 x 30mm Aden Cannon Vs the Yak's single 23mm cannon.
However, while
I would say the Harrier is better, I am biased.