I think you have to give Carter the edge for having the longer career. Barfield's numbers are better, he was better at getting on base and slightly better at hitting for power than Carter (.466/.464), but he only had 4759 career AB to Carter's 8422. At their best, however, Barfield was the better player. Interestingly, 1986 was the best year both players had. Barfield hit more home runs and had a higher OBP and slugging percentage.
Interesting debate. I never thought Barfield was that good.
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