Should I cite a statement as coming from in journal article or from the related PhD thesis? I frequently come across PhD dissertations that have spawned multiple journal papers, either while the author was working towards their Ph.D. or after completion. My field is not one with "stapler" dissertations that merely collate a number of papers, so there are often differences between the details of the paper and those of the dissertation.

However, often there are claims/statements/arguments that are present in both sources, so which should I prefer to reference? Should I cite the earlier reference? The later one? Or are there other issues I should consider?
Personally, I tend to prefer to cite the most recent work, as it is likely to be the most updated and correct.  There is also a good argument to be made for citing the peer-reviewed version (as long as it isn't too much older).  

In general, however, if the two sources are very similar it doesn't matter much which one you cite. There is also no particular need to cite more than one, and I tend to feel it's better to cite only one when the material is basically the same, so that it doesn't look like you're claiming more support than actually exists.