I haven't found any info regarding which of these two cards is the more scarce. Both were issued as #24:
The Elvis alone shot is the same as card #59. The back, though, is the same as the #24 card with the colonel.
Purely speculation, but I'm guessing the colonel card was part of the original run. As he eschewed having his picture anywhere, he probably demanded its withdrawl. Rather than create new artwork, the decision was probably made to replace it with an existing card. The double printed Elvis alone shot can be easily spotted on this uncut sheet image (I stole from an old ebay listing).
As this set was massively overprinted, I'm guessing there are a lot fewer colonel cards out there than any other card in this set. I picked up a couple of closeout sets 30 years ago, and neither of them contained the colonel card. Does your set have it?