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McCarthy's injury might have ended up being fatal but the trauma does not seem to be as severe as Chapman's.
According to a NYT article the next day and the SABR Baseball Biography Project, when he was struck he almost immediately started bleeding from his left ear. He suffered a large depressed fracture of about 3 and a half inches long. I haven't heard exact dimensions of McCarthy's fracture but I do not believe it was nearly as bad as Chapman's. In addition to the skull fracture, he suffered clots which sounds similar to the bleeding that McCarthy suffered.
The biggest difference is medical technology and how quickly a surgery can be performed. The game started at 2PM and he was injured in the 5th inning. This would put it roughly around 4PM or so. Chapman was taken to the hospital where surgery would not begin until roughly 12:30AM and completed about 1:45AM. So it was six to eight hours after the injury before surgery started.
Also, back then of course they didn't have CT scans. Almost immediately upon arriving at the hospital, Chapman would have a CT scan showing the injuries and rushed into surgery. The amount of bleeding into the brain might not be as severe and complications might be minimized.
In 1920, McCarthy's bleed may not have been diagnosed until it started showing other signs hours later. By the time he ended up at the hospital, underwent tests, and surgery, there is a good chance he would not have survived.
So summing up, Chapman would very likely survived the injury if it occurred today while McCarthy's could have easily proved fatal.