Why do the Shi'a have different hadiths?

As is known, there are six major books of *ahadith* used in Sunni jurisprudence. The Shi'a typically don't treat these collections with such esteem, and instead give preferential treatment to four of their own books of *ahadith*. I understand that the Shi'a and the Sunni can have very different ideas about who is considered a reliable narrator of any given *hadith*, which would account for a significant disparity between the two corpora. In addition, there is a general Shi'a rejection of the idea that any book compiled by fallible men can be considered "*sahih*", which flies directly against Sunni opinions of the books of Bukhari and Muslim. However, given that any individual *hadith* would need to be tried for authenticity regardless of the compilation it is in, why then would Shi'a jurisprudence so prefer the Shi'a compilations rather than the Sunni compilations; if my understanding is correct, each and every such volume would still be treated as a mixture of weak and authentic *ahadith*. I am passingly familiar with the Sunni method of determining the health of a *hadith*, typically by analyzing the *isnad* and judging the reliability of each individual narrator and whether any links in the chain are missing, as well as comparing it against similar *ahadith* transmitted via alternate routes. If Shi'a jurisprudence uses a similar method for handling *ahadith*, with the exception that a narrator considered reliable by the Sunni may be rejected by the Shi'a and vice-versa, then I don't understand the need for such disparate collections of *ahadith*. Is there a fundamental difference in the collection and analysis of *hadith* literature which would necessitate entirely different books thereof? If not (or even if so), why is there so little apparent co-mingling of the Shi'a and Sunni *ahadith*?