The movement of air by a speaker is not felt the same way as headphones. Your skin is responsible for picking up some frequencies. For this reason, most gigs have massive subwoofers and line array speaker stacks instead of a plethora of headphones :-)

I am a bass player and I sometimes have to use in-ear-monitoring to stop going deaf, and it isn't the same as hearing the sound from the speaker, particularly if you are counting on the response of the amplifier + speaker combination for sound. Try telling an electric guitarist to use headphones - half of the sound they get is from the combination of amplifier and speaker and the interaction between the two (amplifier sag, speaker cabinet resonance, angle of speakers etc.)