Amazon Web Services has Amazon Simple Notification Service (SNS), being to send push notification via
- Google Cloud Mobile (GCM)
- Apple Push Notification Service (APNS)
- Windows Push Notification Service (WNS)
- Microsoft Push Notification Services for Windows Phone (MPNS)
Here is a post on how to do it in large scale; I find it a good read.
Note that there is a case study of how Parse is using AWS. I wonder if Parse leverages Amazon SNS or the other way.
While it is hard to compare, the following is some pricing information.
As of 11/24/2014, Parse is free if you can live with 30 requests/sec. If you need to push faster, it costs $100 per month for 40 requests/sec.
Amazon SNS is free for the 1st million request per month and $0.50 per additional million requests.