Sorry, but neither of these two reproductions is in any way close to the original. The original Chavet sets are extremely nice and elegant. The repro completely fails to catch that elegance. And the Bundesform repro does not even look similar. It is totally off compared to the original sets from the 1930s. Here is a bit of the true stuff.
Of the Bundesform set, there were different versions, even in the 1930s (not mentioning the more modern variations after the war). The first photo is a Habera version. The second is a version distributed by Hans Hedewig (Curt Ronninger) of Schachzentrale Leipzig.
Here is a setup with a super rare original Posingis chess clock as used in the 1936 Munich Olympiad, in which Bundesform pieces were used.
But talking about your initial question, what other relatively minimalist sets there are, several come to mind. I am exclusively talking about wooden sets, as there are hundreds of minimalist designer sets made of plastic, acrylic glass etc.
The first I would mention is the Berliner form.
Henke made some sets in the 1960s, which were very similar. Here is one from my collection.
Then one would have to mention the Bauhaus chess set designed by Josef Hartwig in 1923.
Another one that comes to mind is the chess set created by Marcel Duchamp.
The Joc Catalan
Then I would mention the so called "Italian Bundesform", a chess set design, which has at length been discussed by Rodolfo Pozzi and Roberto Cassano, both of which have done some admirable research on the set.
And last not least, I have a rather abstract chess set in my collection, which does not have a particular name, but which is a nice example as well, especially since it was made with Karelian Birch, which is one of the nicest woods for chess pieces IMHO.
Have I forgotten anything? Oh yes, I have: the Australian War Memorial chess set and the German "Schlicht-Schach B", which somehow seems to be related. Here are the pictures, I have also included in my book.
Hey, I’m curious what other relatively minimalist chess sets there are akin to the French Chavet and the Deutsche Bundesform.