That's probably a difficult question...
...the Burrito's had a checkered carreer at best and the personnel had changed dramatically over the years...starting pretty much as an offshoot of the Byrds, lotsa' people came and went, so I don't know if one could say the band itself, as a band, was influential, or if was more the premise of a country band with a R'n'R edge...some of the members went on to other groups which did sort of give some direction to the genre of country-rock. If you do a web search of the group, there is more info than I can supply there.
The Eagles have been commercially viable, and that's enough to turn people off to them and their music...there is no "mystique" of the leader ODing or things like that...like Matthew Polk and his speakers, once the darling of the cognescentii, as soon as a measure of success rears it's ugly head, he's a sell-out and his wares are yesterdays news...
They are responsible for well written, well played, well produced music, there is an audience for it and, as Henley said in the NBC show, they have no problem playing the hits...AND more importantly, they can still pull it off...anyone who may have been unfortunate enough to see the one-hit-wonders-revisited show that was touted during the Eagles tee-vee show, will know what I mean.
So, as much as I hate to admit it, simply as an incubator for the genre and some of the more influential players involved in it, my answer would be the Burrito's...BUT I, and more than just a few folks, can whistle or hum an Eagles tune on the spot, can't say the same for The Flying Burrito Brother's...In music, being market-driven, the performers will produce what the public wants, "innovators" sometimes get lost in the sauce...so how do you measure influence?
jimHJJ(...perhaps the question needs a re-think...)
