Forgot to mention the 'content' part. Comedy Club can be as 'clean' or as 'off color' as the audience viewing it, since there is a great deal of audience participation. You'll hear a lot of inuendo, which isn't likely to go over the 15 year old's head. He'll get what they mean and he'll know it's a bit naughty.
Adventurers Club is along the same lines, especially before 10 or 11pm. After that it gets pretty bawdy, depending on the audience. The main problem with kids and PI (in my opinion), is seeing what goes on in the street area. It's not pretty, and sometimes it's REALLY not pretty.
Keep in mind a lot of adults going to PI are there because it's their time away from kids and some of them don't really appreciate the content at Comedy/Adventurers being more stiffled because there are children in the audience. So it isn't just 'what will the kids see', it's also a bit unfair to the adults who paid to get in and can't really enjoy an adults night out in an adult atmosphere. Another good reason to leave by 10pm or so.