Which are the best mathematics journals, and what are the differences between them? Suppose you have a draft paper that you think is pretty good, and people tell you that you should submit it to a top journal. How do you work out where to send it to?
Coming up with a shortlist isn't very hard. If you look for generalist journals, it probably begins:


*

*Journal of the American Mathematical Society

*Annals of Mathematics

*Inventiones

*...?


How do you begin deciding amongst such a list, however? I know that you can look up eigenfactors and page counts, and you should also look for relevant editors and perhaps hope for fast turn around times. Depending on your politics, you might also ask how evil the journal's publisher is.
But for most people thinking about submitting to a good journal, these aren't really the right metrics. What I'd love to hear is something like "A tends to take this sort of articles, while B prefers X, Y and Z." This sort of information is surprisingly hard to find on the internet.
 A: I would personally add Acta Mathematica and Publications mathématiques de l'IHES to the short list.
It is possible to give some particularities of those five journals. For example, Publications de l'IHES is able to publish very long papers (up to 200-250 pages) while there are less common in other journals. Inventiones publishes more papers each year than the other, so it might be a little less selective (although it obviously publishes many top papers). Acta is somewhat shifted toward analysis.
I guess that the best criterion is still the editorial board, as Andy Putman suggested. The probability that your paper is turned down for bad reasons (what I call a false negative answer) is lower when it is handled by an editor that is interested.
A: For submitting papers to "top" journals, I think the most important thing is to submit to an editor who is familiar with your subfield.  Having an editor who can pick an appropriate referee and then understand the report enough to advocate for your paper is essential.
Also, I think it is very important to ask your mentors where you should submit and also which editors would be best.
A: I've heard that Annals tends to like articles that finish off a problem.
A: Look at the "big name" of your field, and if they are still alive, they are probably part of the editorial board of goods journals, to which you should submit your paper.
A: The best journals are the ones that the best mathematicians publish in.  But which mathematicians are the best?  The ones that publish in the best journals.
Seriously, though, one could probably use some numerical methods to generate a ranking of journals or mathematicians from that.  (That may be why this is tagged "eigenfactor".)  And on a more local level, think of the "good mathematicians" in your area, and look at their publication lists.
A: One way of finding which is the best journal is look at the number of citations the journal gets.
A: I seem to remember this being discussed not too long ago on a certain blog not a long way from here ... but then maybe your question is a little more specific than that one was.
To the extent that this information is subjective, I don't think you'll get a good answer.  To make it more objective, you need some way of classifying "this sort of article".  One simple way is by subject, specifically MSC.  Then one can do it by looking at MathSciNet and comparing, say, the last 100 articles published in a given journal.  With a little bit of data munging (technical term), you can figure out which journals publish in which areas.
Unfortunately, if you read the AMS copyright, you can't distribute this information.  In fact, you're not even allowed to keep it on your own computer for very long so you have to redo it every time.
I've got some scripts for automating this stuff here on my website (I hope that putting links to ones own website isn't considered Bad Form here!)
But maybe you have a different classification scheme in mind - do you?
A: AustMS have a journal ranking system where different groups submit their recommendations for what levels certain journals should be ranked at.  Here's the link for pure mathematics.
