The key here is not so much whether consistency with either set of norms is important so much as consistency with user expectations.
From Jakob Nielson's Alertbox:
Consistency is one of the most powerful usability principles: when things always behave the same, users don't have to worry about what will happen. Instead, they know what will happen based on earlier experience.
If you can reasonably assume your users, especially new users, will be familiar with an external convention, follow it. If your system is part of a large suite that has it's own conventions you may stick to them, but this is often not the case; for the most part, people spend their time using other applications.
Another gem from Nielson:
Jakob's Law of the Web User Experience states that "users spend most of their time on other websites."
The quote is focused on web experience but it applies to all software really; unless you're Apple/Microsoft/ect, users are probably using other applications more. There are some industry specific exceptions of course; if you provide a large, common suite of applications or your users likely use multiple products of yours, you might be a "mini Microsoft" enough that your internal conventions matter.
How do you know which case you fall into? Test to determine your user's expectations unless it's extremely obvious which you should be using. If you're Microsoft designing a Windows application, internal consistency is key; users are familiar with Windows, and in that context they're going to be expecting Windows conventions. If you're some random website/startup/ect, stick to conventions when possible.
An important exception is when your application is doing something so different or so much better that you need to create whole new conventions...but then consistency isn't even possible, just make sure you're internally consistent.