Given the averages, most likely Player A will shoot 78, and Player B will shoot 79 or 80. It seems to me that in a single match Player A will have the advantage.
Averages are hard to apply to a single match, scoring distribution and variance is much more applicable to estimate an outcome.
Lets consider both players have played 20 rounds this year, all rounds have been played on the same course from the same tees (72/130). Player A's 20 scores are made up of an even distribution of scores from 76-80. Player B has at least 1 round recorded from 73-86, with the majority of his rounds in the 76-80 range. Player A's average is better, 78 vs. 79.3, but they both have the exact same handicap index of 4.17.
Because player B has recorded scores of 81, 82, 83, 84, 85, & 86, and player A's highest score is 80, we know that player B's average is being dragged down by their highest scores and if player B plays poorly they will always be beaten by player A. But since those scores are not in player B's top 10 they are not used to calculated his handicap.
Also because player B has recorded scores of 73, 74, & 75, while player A's lowest score is 76, we know that if player B plays to their potential they will always beat player A.
Now, since player A's lowest score is 76 and player B has at least 4 scores in their handicap equal or better to 76, we also know that player A's median score is lower than player B's median score. So even within the 10 scores used to calculate each players handicap player B has a higher level of variance than player A. Player A's handicap scores equal 77 +/-1 while player B's handicap scores equal 76+/-3.
Because of the variance in B's scoring compared to A's scoring, if B plays below average they have less than a 10% chance to win the match. At the same time, if they play above average they have nearly a 60% chance to win the match. And if they play well they have nearly a 90% chance to win the match.
On the other hand, player A's consistency always keeps them in the match. Even if they play average they have nearly a 60% chance to win. This is the factor that tells you to bet on A in the long run. If the contest is a 36 hole match, A is the favorite. But in one lone 18 hole match its not so cut and dry.
The form of player B will make all the difference. When where their scores in the low 80's posted vs. when were their scores in the mid 70's? If their recent scores were better than their older scores, they are a player trending down vs. if their recent scores were higher. Now, if their recent scores included both low 80's and mid 70's rounds, then the match would simply be a coin flip.
Rather than just rolling scores out of the handicap range, each score in the handicap range should be weighted to some degree based on when it was shot. The most recent score taken at 100% value and each following score discounted by some rate.