How much battery drain do push notifications cause on Android 4.1? I've got an S3 on 4.1, and I have a lot of apps which have push notifications. This is convenient, but I want to know if 4.1 is set-up to use push notifications efficiently with regards to battery drain. Would having Android 4.3+ use less battery for push? 

I have push enabled for 4 apps. After adding another push one last night, my battery loses 20% in an hour. I am starting to wonder how much battery do push apps really drain.  I noticed some Twitter apps state that while they use push, they use their own server which apparently uses less of our battery.
Push notifications are designed to be the solution to battery draining apps that constantly monitor for data that has changed locally or on a server. Because of this they are very battery efficient. My phone typically will get 20 notifications in a few hours with less than 1% total battery use.

If your having huge battery drain problems, your phone is probably not sleeping properly which is usually due to an app that is preventing the phone from sleeping. I might be able to help you resolve this With some more information, such as Phone, Android version (or ROM if your rooted) and a screenshot of your battery screen after your phone has been running for a few hours. I will update my answer accordingly.