Publish more research papers or advise dissertations? A faculty should advise students working on dissertations and to publish also. However, publications can come from students working on dissertations, from working alone or from collaborating with others like postdocs. So should faculty advise more students working on their dissertations or work with other researchers? It is clear that faculty should do both of them, but should anyone be given a higher priority?
Your question is largely a false dichotomy. For instance, there's no reason a paper written by one of your students can't involve collaborators at your institution or from other institutions as well. 

So long as your students are publishing, and you're establishing a network, I wouldn't worry about trying to prioritize one over the other, unless your institution's promotion and tenure regulations have something specific to say in the matter.