Specialist290 was correcting us (thanks!) and the Civilopaedia. It says JSB decreases unhappy citizens by 2 per city on the same continent. It should just say 2 per city (the continent doesn't matter). I am not sure that JSB is related to cathedrals, though.
Yes, JSB is very similar to HG, except HG only affects 1 citizen per city. Also HG expires eventually and JSB doesn't. And HG adds a happy, rather than removing an unhappy. I am not sure there is much practical difference there, but maybe someone will tell us.
On higher levels like Deity, with high populations, it is not true that everybody's always happy, even with these wonders. But they do make a huge difference. Personally, I like Mike's (Michaelangelo's Cathedral) with a really big civ.