The only magazine that gave LIFE a real run for it's money was LOOK magazine. Started in 1937, LOOK magazine lasted until 1972. It was a large size magazine at 11x14. It was mostly known for it's photography, but was always considered by some as an "also ran" to LIFE.
The magazines biggest chaim to fame is that Stanley Kubrick was a staff photographer there from 1946 to 1951. Just before his film career took off.