I imagine that Rivera never faced the same batter twice in a game, at least as a reliever.
When complete games were more in vogue, starters were obliged to face the same batter four or or five times in a single game. Batters catch on and adjust, so those starters had to adjust and vary their approach in subsequent at bats. The good starters prevailed in subsequent at bats. The not so good starters became progressively less effective. Perhaps a little too simplistic, but a starter may use his fastball as an out pitch the first time through the line up and his curve or slider the second time through the line up. In Men At Work, George Will writes about Orel Hershiser's approach as he progressed through a game, which details his approach to batters the second and third time through the line up.
Pitch counts and analytics have shortened the starters time on the mound, but today's good starters can still be expected to face some of the same hitters at least three times on a good day.
If a batter faces roughly 5 pitches per at bat, then in the ninth inning he sees only five of the closers pitches. In the first eight innings, if the starter is on his game, he must throw that same batter 15-20 pitches and retire him three or four times.
Rivera was a very good ninth inning pitcher, perhaps the best we've seen, but to compare him to the best starters of any era is a stretch in my opinion.
As I suggested in the Twilight Zone, analytics going forward may lead to continued and further shortening of the starter's time on the mound. When we get to the point where no pitcher faces the same batter twice in a single game, then it might be reasonable to compare starters and relievers on a more level playing field.
