Suppose that a conference paper already has a MathSciNet review. If later that paper appears with the same abstract in a journal, what is the point of making a new review? Also, wouldn't it make more sense to first ask the person who made the review for the conference version? (In a way, of course it's better to have different opinions, but with this mentality everything could be reviewed twice, so this is irrelevant here.)
At the moment most of those decisions come from me, at least for computer science papers (those with a 68 class as primary). The practice of having proceedings and final versions of papers is not exclusive to computer science, but this is where it is most common.
I've found more often than not that the journal version is significantly different from the proceedings (not just in the straightforward sense that it contains proofs omitted from the first version due to page restrictions) so, if only one is reviewed, the journal version is the obvious choice.
Unfortunately there are many wrinkles. There are papers that appear in proceedings and a final version never makes it to a journal. Sometimes we do not receive the proceedings version until after the journal version has been reviewed. Sometimes the title changes or for some other reason we fail to identify that one corresponds to the other. And yes, sometimes there is no discernible difference between both versions, and I do not notice this, or I notice it and feel it may be something a reviewer may want to point out explicitly. Etc.
Lately, with a few exceptions, I've been trying to only have the journal version reviewed. This has been traditionally how this situation is handled. If there seems to be a need for a review of both, I usually try to contact first whoever did the first review; I agree this is the natural choice of reviewer. However, this person is not always available. And sometimes, a different reviewer makes more sense once the details of proofs reveal connections not highlighted before.
Anyway, please feel free to email me (to my AMS account) if there are specific papers that concern you in this regard. And any comments or feedback you may have would be most appreciated as well.