Should I publish a given unit of work in more smaller papers or fewer larger papers?
In math it's generally better to aim for fewer, longer, better papers.  There's nothing wrong with publishing short papers if that's what best fits your discoveries.  However, given the choice you should not publish your results piecemeal as you derive them, but rather try to collect and polish them and craft coherent, substantial papers.  There are several reasons for this:


Publishing partial results piece by piece makes it harder to write understandable papers.  A few papers later, you'll wish you had done things a little differently, and you'll start writing things like "by the same idea as in the proof of Lemma 3 in [15]" because the statement of Lemma 3 doesn't quite say what you need now.  But it's too late to change it, so your next paper is either cryptic or repetitive, and neither one impresses readers.  Or you find an ad hoc way around it, but your paper ends up being a little less natural.  Basically, this is a form of technical debt.  Once you have enough technical debt, the only good solution is to write a clean exposition from scratch.  Every topic eventually reaches this point (which is one reason we have expository papers and books), but in the meantime you'll minimize the problems if you gather related ideas in one place and write them as a coherent unit.  
If you break your work into papers in unnatural ways, you risk looking desperate for publications.  Each individual paper may look like you don't understand the big picture or don't think your work is going to amount to anything substantial.  These are not messages you want to send to readers.
If you want a serious research career, you need to publish in good journals.  Taking a long paper in a prestigious journal and breaking it into three short papers in less prestigious journals is bad for your CV.  Experts might know those three papers amount to something substantial when combined, but a non-expert looking at your CV won't be able to tell.
Many people in your subfield will form an opinion of you without having studied your work carefully.  For example, plenty of people who have never read any of your papers will see you give talks at conferences or will see references to your work.  Because they don't have a global context for your work, to a first approximation they will judge you by how good they think your average paper is.



  One would think that if I "subpublish" that actually since my results become available more immediately that it would benefit the community if I did so.


If you reach a nontrivial milestone that is genuinely exciting or useful for other people, then that could be a good reason to publish a paper now, rather than sitting on the result while you try to complete a larger project.  On the other hand, there's much less value in presenting a steady stream of partial results taken out of context.

Of course career pressures sometimes interfere with ideal publishing.  If you're going on the job market soon, then writing a suboptimal paper now is probably better than writing an optimal paper later.