The age old debate. People who learn note for note have no creativity. People that don't learn note for note are lazy. There's probably a little bit of both going on.Some would say that those who have to learn it note for note have no creativity.
Just my two cents, but if you are in a cover band trying to maximize income, you should learn the songs closer to the original recording. If you are just in it for fun and/or to make music, I wouldn't worry as much.
As to the audience or other musicians noticing, I know for a fact that many musicians don't notice. There have been many, many times over the years I've been told by people I played with that I nailed a part that I knew wasn't exactly right. To think that most non-musicians can tell the difference between a part played close and a part played exact is really just silly.