to publish paper is much easier than to register a patent and I think it is less in cost than registration of a patent, However the patent could bee bought by a company ore institution and can give a good economic value , be clever and publish a paper without your patent and then after think about how and when to register a patent
I think that a patent can only be applicable in research related to physical, chemical sciences or biological, but for social sciences a good research work publication in available good journal. However, patent followed by a good publication is not a bad idea where ever it is applicable, as you may get royalty for your research work if there are people ready to use it in future and peer recognition is an added benefit for others.
A patent is more worthy than research publication and based on researcher invention, whereas the publication can be possible by research. Can be define that : Patent = research + Tiral registry. Thus, both are equally important..