One thing I know about when it comes to push-ups vs barbell bench press, is that (amongst many different muscles stressed), one group of muscles that are taxed, and taxed superbly is the group called the Serratus anterior.
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Do a normal set of push-ups taken to failure, then rest 20 seconds and do as many more reps as you possible can (usually 3-5), rest another 20 seconds and see how many more reps you can do. Call it a day and feel your serratus anterior the next day like you've never felt them before!