My hunch is that the second one is early 50’s and the first one, with Constante’s portrait, is mid 50’s, published after the great man’s death. I believe there’s a third one in the (probably) 50’s series in the Cocktail Kingdom Library.
I could, of course, be completely wrong. I’m certain, though, that the second one is a Bacardi promotional. I’ve done recipe by recipe comparison and the main difference is that the second features about ten extra Bacardi drinks that are clearly marketing drinks (Bacardi Mint Julep, Bacardi Mojito on top of the regular Mojito, etc). The dedicatees have all disappeared but it could be precisely because it was a promotional edition, and not a regular one for friends and regulars. This being said, cocktails named after people have also been expunged – as was the ‘Vermouth Colonial Style’, so who knows…
For what it’s worth, Fernando dated the first one to early 50’s and the second to 1956, but I don’t know on what basis.