One thing to keep in mind is to see if the browsers have the ability to render/open the document in itself (built-in feature or via 3rd party plugins (Adobe Reader or Foxit PDF Reader) without having to engage an external application on the host operating system.
If the browsers can open the document in itself, then you have access to the back button which will take them back to the previous page, which is good UX. If the document opens in a new tab, then there's a risk that it might get blocked if the browser deems it to be a pop-up.
Also, if the user wants to view multiple documents, it could get a little annoying with all those extra tabs that will crowd the browser. Or else, the user will have to close every tab after she is done with it, which could also be tad bit cumbersome when compared to just hitting back on the current tab.
My recommendation would be to open it in the current tab.