Mathewson pitched from 1900-1916, winning 373 games for the New York Giants. (He pitched in, and won, one game for the Cincinnati Reds in 1916.) Alexander pitched from 1911-1930, winning the same 373 games while pitching for the Philadelphia Phillies, Chicago Cubs and St. Louis Cardinals. Mathewson had a .665 winning percentage to Alexander's .642. (Alexander had 20 more career losses.) Alexander, who pitched for three more seasons, had more innings pitched in his career. (5190-4788 2/3) Mathewson had more strikeouts (2507-2198) and had a lower ERA (2.13- 2.56) and gave up a lot less homeruns (165-89) than that of Alexander. Alexander had slightly more complete games (437-435) and owned a 90 to 79 edge in career shutouts. Both pitchers had dominant WHIPs. (Mathewson 1.057, Alexander 1.121) Mathewson won 30+ games four times in his career, while Alexander had three such seasons. Mathewson had 13 20+ win seasons and Alexander finished with 9 in his career.
The stats would say that Mathewson was the more successful pitcher. One thing that has to be considered is the eras that they pitched in. It is easy to say they pitched at the same time since it was all so long ago. But Mathewson pitched his entire career before 1920-1921, which was considered the beginning of the "live ball" era. Alexander pitched the first half of his career in the "dead ball" era and the second half in the "live ball" era. The fact that Alexander gave up almost twice as many HR as Mathewson has a lot to do with Alexander pitching ten years when homeruns were a big part of the game. But, with more homeruns came more strikeouts (still no where near as much as are in the game today) and because of that, the fact that Mathewson struck out many more batters than Alexander in less innings pitched was extremely impressive.
Interestingly enough, Mathewson was sent to the minors in 1901 and drafted by the Reds, who traded him back to the Giants. Of course, Mathewson would pitch the one game for the Reds in 1916 before taking over as the team's manager for the next three seasons.
Alexander is known for his performance for the Cardinals in the 1926 World Series. After pitching games two and six, he was called in from the bullpen with the Cardinals up by a run in the seventh inning of the seventh game with the bases loaded, two outs and one of the best Yankees hitters at bat, Tony Lazzeri. Manager Rogers Hornsby tried to advise him how to pitch the batter. Alexander disagreed, saying he would pitch with a fastball in (which was where Lazzeri liked the ball) then pitch him off speed away and finish him with another fastball in. Hornsby reportedly said, "Who am I to tell YOU how to pitch?" Lazzeri was struck out on three pitches despite almost hitting a homerun on the first fast ball. Alexander finished off the final two innings to lead the Cardinals to the World Series Championship.
Both pitchers are legends and are part of the best pitchers to ever play in this game.