My interests primarily pertain to Astrophysics (and Astrochemistry). This subject appears to have two masters: Physics SE and Astronomy SE. How do I decide where to post, and how would you characterize the astrophysics sub-community on each SE? Does double posting of Q's make sense? I will be posting this meta-Q on the other meta-SE also.
It depends on what the question is about. I sometimes have to make this choice, because I'm reasonably active on both sites.
There's a substantial amount of temptation to go where the user base is. There are, without question, more astronomers and astrophysicists studying at an advanced/professional level and actively answering questions on Physics Stack Exchange than there are on Astronomy Stack Exchange. Most of these spend their time exclusively on Physics, although the one notable exception is Rob Jeffries, who joined Astronomy this past year and has been avidly answering questions ever since. So it's possible that you're more likely to get a question answered by a professional if you ask it on Physics than if you ask it on Astronomy.
Why? Well, the relative sizes of the sites is certainly the major factor. It's evident in other ways, too: Physics has 783 questions tagged astrophysics, while Astronomy has 48 questions tagged astrophysics. Even taking into account the fact that Physics is older, it still has a higher rate of astrophysics questions coming in (although it has a higher percentage of unanswered questions, though not by much).
How do I decide where to post
This is your call. However, I would recommend going to Physics from a purely chance-of-getting-the-question-answered standpoint.1 For astronomy questions, though, I would absolutely recommend Astronomy.
how would you characterize the astrophysics sub-community on each SE?
The astrophysics community is stronger on Physics than on Astronomy. Same with chat, by the way. I often take minor astronomy/astrophysics questions to the Physics chat room instead of the Astronomy chat room.
Does double posting of Q's make sense?
It's been said in the comments that this is a bad thing, so I'll just reiterate: In most situations, cross-posting is a bad idea.
I will be posting this meta-Q on the other meta-SE also.
I'm not sure if agree with this. Having two discussions will help get the input of both communities, but it also splits up the advice you'll get.
1 That said, more astrophysics questions would certainly help Astronomy. . .