I would say that 社会 pretty much matches "society" in it's most general sense. 世の中 on the other hand if often used in fixed expressions such as 世の中は甘くない and more readily lends itself to "world" as a translation and in such expressions.
Yeah, I feel like 世の中 tends to be used to talk more about trends or views in society, whereas 社会 is more just generally referring to society itself. Another phrase I've seen is この世の中だからこそ~ "Because the world/society is like this, _____"
社会 also tends to be used in compounds to do with society such as "social movement":社会運動(しゃかいうんどう)、"social problem/issue":社会問題(しゃかいもんだい), and I would say seems less "idiomatic" and general than 世の中.
世の中 vs. 社会
Can anyone offer any information on how 世の中 and 社会 differ, connotations-wise, as they're both listed as meaning 'society'?