Hi Tarek, I'm posting this after ST's posts so if it appears out of sync please refer back to his and Prakash's posts.
I spotted a couple of inconsistencies, IIRC the max SPL of the S1 is 109 dB (It is very hard to find detailed specs, this number is not given on the web page or in the manual) the 103 dB quoted is continuous, the JBL figure of 112 is pretty much certainly max (and is incorrectly described as sensitivity in the spec). 9 dB is a very large difference, 3dB is small enough to be more or less irrelevant.
The tweeter in the JBL is an HF driver, they don't quote a crossover frequency but typically it would be around 1200Hz or higher so barely overlapping into the high mids, Bose don't quote a crossover frequency either but it's entirely likely that it's lower as the Bose 'tweeters' are cone speakers rather than horns.
JBLs frequency response figures (of 37.5-20,000 Hz) are meaningless as they don't specify limits (the Bose don't quote figures in the brochure/manual/webpage but if you search hard enough you will find them and they do give limits, IIRC /- 10dB and /- 3dB for the S1)
Now a personal opinion, those who know me on these forums know I am not a Bose 'fanboi' by any stretch but, apart from a couple of specific issues* I do like the S1 Pro (and the L1 series, though I don't own any). However I tried the Eon Compact and S1 Pro side by side at a point when I would gladly have returned my S1 Pro. I really wanted to like the JBL as it has so much going for it, especially the onboard iPad controlled mixer (a huge plus IMHO). But I simply could not get on this the sound, whatever I did to the eq it sounded harsh and 'edgy'. This made it a total non-starter for me, if QSC or Yamaha build something similar in the future I will give it a listen as their house sound is, to my ears, much nicer than JBL.
If you like the JBL sound then buy it, the slightly better LF and built in mixer would make it a no brainer for me but the most important thing about a speaker is the sound and the JBL does not stand up for me.
* The infamous 'battery drain issue' which is, for all practical purposes on my S1s at least, fixed and the less well documented wayward bass, the S1 is remarkably capable when it comes to LF but getting good bass out of a tiny box requires some trickery and, to my ears, the bass ends up over hyped and inconsistent, it is also completely useless for bass guitar at any useful volume, but that's not what I bought it for so that latter is fine.