Are there any hard and fast rules as to how to assign relative importance of one authority over another in formulating a psak halacha? For example if the Rambam and the Rashba argue over a specific halacha to whom would a posek give more credence and on what basis? Are there blanket generalities or would we, for example favor the Rambam in hilchos Shabbos and the Rashba in shechita?
Generally, (especially in arguments that take place in the Talmud), we generally view the older source as priority. In your case, Rambam would have spoken before Rashba. (Since Rambam died in 1204, and Rashba wasn't born until 1235, I make the assumption that Rashba argued with him posthumously, which happens often). So I would say, at the most general level, Rambam's word would be prioritized, but there are other factors that you should take into account that are specific to the text your referring to. But as a basic rule, who said it first?
However, as has been pointed out to me, הלכה כבתראי sates that within the same halachic period the newer source would be better, since whoever wrote the newer source has read more opinions than the person who wrote the older source.