Both sticks look the same as far as the design on the butt. One of the sticks has a black ferrule and one white. Ivory cracked so he replaced it with a plastic of some sort. He looks older in the top as he is wearing glasses so that may have been the case.
The picture shows the butt of Wimpy's cue below the table and it appears that the cue doesn't have a wrap on it or are my eyes playing a trick on me. That's a great picture of Wimpy by the way.
I don't think it's missing the wrap, as I believe that's the cue I saw him playing with in Atlantic City in 1982, and it had the wrap,quite aged. It could be the white ring above the buttplate looks a bit oversized or blurry, as white does in pictures. If you look up videos of Lassiter playing Boston Shorty and Cicero Murply, it looks like this is the cue he's using, and it has a wrap. As has been noted above, it's not crystal clear whether the cue is a Bushka or a Tad.