One thing I've been doing is playing a cover tune then a few songs later, playing the original in what I announce as "The cover project." No judgement one way or the other, not much commentary but to highlight what is the cover project.
The rules, as I layed out, is that I announce it as the cover project and play both versions. I also don't play them back to back. I usually try to build them into the flow of the set so as not make it seem like it doesn't fit in the show.
Here you'll find my take on how the covers rate in comparison.
John Denver's "Poems, Prayers, and Promises" covered by Rachel Halden.
This is not a bad cover, but John Denver's soft, plaintive tenor really steals the show. You can actually believe that John Denver is sitting around a fireplace in his Aspen, Colorado home trading stories and smoking pot with his friends. So, in a way, the cover doesn't catch the intimacy of Denver's rendition. Is the cover better? Absolutely not.
Bob Dylan's "Visions of Johanna" covered by the Old Crow Medicine Show.
There are a lot of Bob Dylan covers that are better than Dylan's versions. Even hard-core Dylan fans may reluctantly agree that Jimi Hendrix's "All Along the Watchtower," or Jim James & Calexico's version of "Going to Acapulco" outshine the originals, and in Watchtower, Dylan's version is really a very good song. In light of the fact that Dylan is an acquired taste and in light of the fact we are comparing a live version to a studio version, I think Dylan's version wins if only because Dyland was still making records that mattered to him in the early '60s. If you were to pick a later cover, you could argue that Dylan had moved into a lazy, almost casual recording style that meant the quality varied from album to album (think post "Desire" Dylan), but this Blonde on Blonde, which almost everyone should have in their collection.
Sonny Rollins' "St. Thomas" covered by Ray Obiedo.
It's almost unfair to compare these two. Rollins' version is from his classic Saxophone Colossus while Obiedo is from his relatively obscure Latin Jazz Volume 1. Trade the tenor sax for a vibraphone and you have a tune that really belongs in the Caribbean. Is that enough to unseat the original. Nope.
The Band's "Acadian Driftwood" covered by Shawn Colvin.
This is hands down one of the more beautiful songs in a catalog of beautiful songs. And while Shawn Colvin does an admirable job, the Band's version wins. No discussion necessary.
If you have a suggestion for a really good cover, drop me a note in the comments.