Photo credit: Lucasfilm
Boba Fett has surprisingly little screen time in the Original Trilogy, just 2 minutes and 45 seconds (2:55 if you want to count the SE Episode IV). Episode II helps him out with an additional 2:15, bringing us to a film total of 5 minutes and 10 seconds across three (four with SE) movies.
Though I am focusing on the films here, I do want to mention that young Boba Fett does get some exploration in the period between Attack of the Clones and Revenge of the Sith thanks to The Clone Wars animated series. The young clone can be seen in seven episodes, and is voiced by actor Daniel Logan who played the character in Episode II.
Captain Phasma has two equal sums of 1:45 giving us 3:30 minutes so far. A huge part of me wants to count the deleted scene version of her encounter with Finn in The Last Jedi, but that would be cheating. I will endeavor to follow my rules, even if Phasma would approve of the deception.
The Chromed Captain also appears or is mentioned in four episodes of Star Wars Resistance causing trouble for Kaz and Poe as the First Order tightens its grip in the space around the Colossus Station. It is interesting to note that if you split up the trilogies, Phasma does have more screen time in the Sequel Trilogy than Boba Fett has in either the Prequel or Original Trilogy.
Advantage: Fett clocks in with more time on screen giving him the clear advantage here…so far.