Where is Tom Henke at? This guy has better numbers than people in the Hall of Fame and he pitched in a tougher era. He never had a bad season and was really good even in his last season, in fact he was the relief pitcher of the year that season. Henke has a better ERA, WHIP and more strikeouts and saves than Bruce Sutter. The only thing Sutter has is 252 more innings pitched but that just shows how much better Henke was, that he was able to accomplish more with less innings. From '85 to '95 he was a lights out reliever. Henke should be in the Hall of Fame, and since he isn't he should be on the list here.
Bruce Sutter won a Cy Young in 1979 and was in the top ten in voting in four other years; Tom Henke never finished in the top ten for voting. Sutter led the league in saves five times and had 35 or more saves in a season three times; Henke led the league once and had as many as 35 saves in a season once. Sutter was also one of the first to popularize the modern split-fingered fastball (which grew from the old "forkball," which, appropriately enough, Henke threw).
I'm not saying this makes Sutter better than Henke, but they are probably the reasons why Sutter was elected: "black ink" recognition as a league leader multiple times and some hardware with the Cy Young. Relievers are a dicey proposition and Sutter is still considered by many to be borderline.
But with respect to the number of innings pitched between the two men, you might want to re-check what you mean by "accomplish[ing] more with less innings." In 14 seasons, Henke pitched in 642 games for 789.2 innings while in 12 seasons, Sutter pitched in 661 games for 1042 innings. If you look at the last six years of Henke's career, from 1990 to 1995, there is a pretty close one-to-one correlation between games pitched and innings pitched, which corresponds to the practice of using the closer for only one inning. By contrast, Sutter approaches that one-to-one correlation only in the last two years of his career, when he was used sparingly, anyway. This corresponds to the old-school argument, used for relievers from Hoyt Wilhelm to Rollie Fingers to Goose Gossage, that closers "back in their day" used to pitch two- or even three-inning saves regularly.
Qualitatively, though, Henke posted some serious numbers. He and Sutter have roughly equivalent career WAR numbers (baseball-reference.com version), but Henke has the superior ERA+ and strikeouts per nine innings pitched. (By a curious coincidence, each pitcher struck out the same number of batters: 861.) That might indicate the deficiencies of how relievers get evaluated (saves are a cheap statistic) more than anything, though, which also indicates the reluctance the Hall has with specialized roles such as relief pitching. I don't think Tom Henke should have been a one-and-done on his only ballot appearance in 2001, and if he isn't on the list of "not-ins" on this site, perhaps he should be.