The general rule is to use push notifications if the app does not update regularly (at specific time of day) or not so often.
But what does this mean in simple words? What is this time interval said in hours/days/weeks/...?
In other words, based on the frequency a certain app updates its content, how can I decide if I will implement pull or push notification service?
PS. when I say pull, I refer to a regular mobile service which contacts some web service which usually sends data to that specific app.
Well, it's up to you and specyfication of your app. You should use push instead of pull if you don't know when messages will be sent or if it's important for your application to deliver content to users immediately after it was created. In general, using of push is not determined only by requests frequency. You can of course mix this two methods depending on content that you wanna deliver to your end users and e.g. use push notifications to notify users that there is new content or that they just received a new email or sth else.
Hope it was usefull...