I agree with @Jacktionman that you should provide an option for your users to choose between the behaviours; however I would say that if you're going to mandate one you should stick to separate notifications.
The problem is that while consolidated notifications might look prettier they convey less information to the user, and may force him to undertake actions which he might not have wanted to.
I'll use the Google Hangouts app as an example: if you have one unread message and you look in your notification drawer you will see that you have an unread message, who it is from, when it arrived, and as much as the message text that can be crammed into the description (my Note 3 seems to flip a coin between ellipses and expanding the notification so all the message fits on, but I digress...)
However, if I then receive another Hangouts message, then all of that information is taken away from me! I am told that I have 2 unread messages and that is all. To get the same level as information I had as when I only had one unread message then I have to tap the notification to go to the app. This cripples the at-a-glance convenience of the notification drawer.
Furthermore, in some apps the act of activating the notification will trigger some further action in the app. To continue the Hangouts example, if I open a conversation thread then Hangouts will inform the other members of the conversation that I have now read all previously sent messages and leave them expecting my reply; when the truth of the matter might well be that IRL I had the chance to quickly glance at a message, but am not currently in a position to reply.