We use our own server scripts for Android and iOS. Android is super simple and works very very well. Apple Push Notification Service (what EasyAPNS is made for) is fairly horrible. We have had a hell of a time with it and are moving to EasyAPNS which might be easy for someone with fairly extensive background in server IT, but not me
Main problem with APNS is that we send messages to the APNS servers just fine but for unknown reasons sometimes users just don't get them. Apple does not report any errors other than uninstalls/unregisters of your app/push token. In my opinion it is crap.
Apparently if you have better volume then APNS is mostly more successful. The kicker is that you will never know when it fails to be received by the user. So keep that in mind when setting up the notification system. We have reminder notifications go out for when players don't make their turn in a certain amount of time to help with this.
Tell me if you're looking at GCM or APNS and I can point you in the right direction for stuff. Also do you plan to send them on demand like one at a time or can you batch them and send periodically?