To be sure, even in Armin's revised timeline, the earliest script Coca-Cola logo is very similar to today's version, where the Pepsi logo went through many drastic changes. This, rather than absolute accuracy, I believe, was the point of the original JPG.
And Pepsi is sure to have at least another drastic change in the future since I don't know a single person that doesn't think the current logo is terrible.
To me, it's not even the logo that's the problem with their current branding (as represented on actual bottles/boxes of product); it's the fact that, given the solid, sparse colors and the lack of copyright emblems or extra PR-shpeel on the label, they look like a no-name brand, a cheap knock-off of themselves made by a company that's not allowed to be them.