Summarizing the reviews from Thomann and some reviews from magazines, it seems that the JBL Eon Compact has a certain advantage with bass, which reaches deeper and is obviously a bit more powerful, however the clarity of the mid frequencies seems to be better with the Bose S1.
I find both quite interesting, but the price point for a stereo pair is steep, so I still prefer a HK Nano 605FX, which certainly has more power, too.