I have no personal experience with either of these kits to offer, only my past thoughts when I have considered making a tambour (never got around to it).
I like the clean lines and interlocking nature of the Amana kit, but I have real concerns that if the tambour was ever subject to some abuse (or if it were to stick and get tugged on hard) that the balled-out sides would be the weakest part of the tambour and subject to splitting -- which would ruin the assembled tambour. Unless, of course, you wish to thread a cable through the tambour like a traditional tambour, but then that kind of negates the benefit of the interlocked slats. (Even so, there is still the risk of splitting the weakened sides of the balled out end, but atleast the threaded cable would prevent the entire tambour from failing due to a split.)
The traditional approaches of backer cloth or threaded cable provide for a far more robust and redundant tambour design. You would have to pretty much destroy a traditional tambour before it would be rendered unusable.
If a simple tambour design would suffice, I would think a round nose bit and matching round over would suffice. Then make a jig for the dril press to drill the holes for the cable to be threaded through and you have a complete tambour without the need for a cloth backing -- not to mention a couple of inexpensive router bits that can be used in many other projects.
Just my thoughts.