Gillette "NEW" with common bar handle ("long comb")
Gillette "single ring" ("short comb")
From what I've been able to gather, the reason for the comb was its effectiveness in shaving around heavy growth (the ample sideburns & mustaches of our forefathers), and less apt to clog. More blade is exposed, too, leading some to feel the open comb razor to be more aggressive than the solid safety bar razor. I tend to agree. Other folks swear by them, though.
Gillette "Goodwill"
Gillette continued producing open comb razors when it introduced the first "twist to open" (TTO) razor, the Aristocrat, in 1934. This, along with the Sheraton and Senator (as well as several British models), continued until the advent of the Regent and its solid bar around 1940.
1937 Sheraton
GEM Micromatic open comb
Note: The early Gillette open comb razors were susceptible to cracks forming in the handles at the base and near the neck, as they were hollow tubes with the base and neck fittings pressed into them.