I personally like both strainers.
The Zoomatic is the "nicer" of the two but is more complicated and has more parts to tear up and to be lost. It can also damage the shell more easily if over tightened. It works great if used properly however. The butt plate usually found with this strainer (during this era) has a bar that extends the wires past the head.
The rapid strainer (on your drum) is just a more simple design that works great with less issues.
There are a lot of examples of the strainers on this site. You can click on Vintage Drum Identification then Drum Hardware then Slingerland.
Hope this helps.