I agree with @Dan Romik's answer. I also want to say that in this set of circumstances, it does not really seem necessary to take any heroic actions in order to acknowledge priority: since the OP's paper was published more than a year earlier: okay, as the record lies, the OP has priority.
I agree that the OP should make sure that the community knows that s/he had the stronger result first, and that contacting the authors of the later paper is a good idea. But I think the OP should do this with a winner's grace: this is going to be much more awkward and painful for the authors of the later paper.
I also want to mention that this kind of thing happens in mathematics all the time. For instance, a few days ago I found out that the main result in a paper I published a few years ago appears, in much stronger form, in some "Lecture Notes" from 1974 (that were apparently never formally published: they are not listed on MathSciNet). Well, gosh. I haven't decided exactly what to do about this, but please be assured that I am not rubbing my hands greedily at the thought that my too-complicated-partial result has "priority" in some formal sense.
Added: Concerning the author's
I have often seen journals publishing short notes with the title "Acknowledgement of priority", in which it is explained that a published result was already proved by someone else, but I have no idea of how it works.
I did MathSciNet searches for "acknowledgement of priority" and "acknowledgment of priority" and got 62+25 hits. When you remove double counting, false positives and papers analyzing priority disputes from long ago (e.g. Euler versus d'Alembert), you get about 70 genuine instances of the sort the OP describes. Restricting to theoretical mathematics over the last 30 years, I found 9 genuine acknowledgments of priority. Moreover, among the entire group of 70, only a few are written by someone other than the author of the original paper.
From this, I would suggest that "the way it works" is that the author herself must be moved to make an acknowledgment of priority, but that this is done only in a small minority of cases. As I said, above, I am myself considering writing an acknowledgment of priority. If I do so, then in view of the above numbers I will be a world expert on the subject, and I will add more details to this answer.