I am planning to use ionic to to create a hybrid chat app. Which one should i use to implement push notification and realtime chat. Either parse or pubnub or both. can i just use pubnub to achieve both functionality?
Ionic has it´s own push notification service in alpha state. You should give it a try. Seems pretty awesome and easy to implement.
Personally I have built a chat app with firebase and it works out of the box. There is also a full tutorial how to implement it.
Parse is a great choice for push, but you can send push notifications using PubNub JavaScript APIs too.
I actually write a few tutorials on hybrid mobile chat apps (using Cordova), also tuts for push notifications with GCM and APNs:
http://www.pubnub.com/blog/converting-your-javascript-app-to-an-ios-app-w-phonegap/
http://www.pubnub.com/blog/sending-ios-push-notifications-via-apns-javascript-using-apns-phonegap/
I wrote a tut for for Android with GCM too, if you want to check out :-)