At first glance it seems obvious that if choosing between "something" or "nothing" it is better "something", even if that "something" is outdated. However, this depends on the value your app has.
Are there any disadvantages for the user not being able to see old news?
Outdated content might be worst than not showing content. Think of a weather app, it might be convenient to use a range in which if the user didn't retrieve the latest information in the last X time, the (old) information the user has might be inacurate/wrong. So it is better not to show that information and ask the user to connect.
Balance what the user wants from you in the long term:
If the user is expecting accurate and latest information over anything else, then it might make sense not to provide cached content after a period of time.
If the user is expecting news to read, preferable the latest but old ones are also ok to read, then not having news cached might not be the best option.
If you choose the first option, consider some period of cached content, whether it is 1 minute, 1 hour, 1 day, etc.
Always show the Last Updated time so the user is aware of it. Also provide an easy way (pull to refresh) to update.