How to decide between sending paper to a specialized journal or to a journal with broader audience? I work in mathematical physics. Typically, papers in my field are either published either in general math journals (Annals of Math, Transactions of AMS, Proceedings of AMS) or in specialized math physics journals (Communications in Math Physics, Reviews in Mathematical Physics, Annales Henri Poincaré, etc.) Personally, I have had papers published in both types of journals. Yet I don't have a good sense whether a particular preprint should go to a general journal or a specialized journal, so I usually just pick at random. 

What are the factors one thinks about when making a decision between submitting to a specialized journal and a general journal of similar quality?
I tend to think that in most cases, the specialized/broad dichotomy is not very relevant. The most important point is to send it to an interested editor; if the most relevant editor for a paper happens to be at a general journal, you will often be better of sending your paper there.

I would consider two exceptions to this principle. First, top specialized journals are usually less reputed than top generalist journals, so if you get a truly impressive result, you may want to get the best of it by sending it to a top generalized journal. Second, some generalist journals will turn back papers that seems much more specialized than the average math paper (e.g. when the basic objects you study are unheard of by most mathematicians).