He did a credible effort. But, just not the same. Of course, it couldn't be.
First of all, there have been several noteworthy members of the Eagles. Many bands are NOT at their best, live.
Presumably Gill is the right pick for now, for his ability to harmonize with the others--that being the hallmark of the Eagles, all along. Plus he is tight with Henley, I think.
Did you know the Eagles group started backing up Linda Ronstadt in LA, and playing some Jackson Browne songs? 70-71.
Nobody in the band was originally from California, but it jelled there, presumably due in part, to the studio resources.
Plus Vince Gill is a very highly respected guitar player, another hallmark for the Eagles.
Here he is with a good Eagles tribute band, called Eaglemaniacs
http://www.youtube.com/watch?v=r7WOJwhVfLs