It all boils down to typical American Gung-ho versus British understatement.
Man for man at the most basic level, the RM excels, as (almost) every British marine is a commando.
No every US Marine is trained to the same standard as a ranger (the closest thing the US Military has to a RM Commando or a Para)
However, the RM certainly doesn't have a signature tune like the "Marine Corps Hymn" which many around the the world are familiar with http://hk.youtube.com/watch?v=za2jp_tfifs&feature=related
Any one remembers how RM's "A Life around ocean waves" sounds? Let's remember PR is potent PsychOPS too.
RM is brigade size comprising a number of light infantry "commandoes" (battalions), USMC is a huge combined arms force of three full divisions with organic armoured units, plus three division-size air wings and three division size support formations (hence all commanded by 2-star generals). An RM commando will always be a commando, a US Marine, having the "right stuff", can choose to become a fighter pilot or even an astronaut, and yet every US marine is still a profiicient combat rifleman. The first American to orbit earth in space was John Glenn, a marine aviator.
RM Commando was not in existence before WWII, and commando units were shared between the Army and the RM during the War, only after WWII did commando units were brigaded under RM. Before WWII, for most of the time RM provided security for naval installations and served as boarding/securities parties on naval vessels
I love RM too, especially the commando dagger qualification badge, but comparing it with the USMC will be like comparing a small agile be graceful Lotus with a fully-loaded 5000 cc Trans Am - very different styles - and each has its own fans