I realise this thread is quite old now, however i just wanted to share my experience.
I downloaded an app called Angry Birds Backup by Sergio Patricio which was also free.
This app does backup ALL Angry Birds versions and seemed to work first time for me
This is what I did:
1) Downloaded the App on my old phone (HTC Desire).
2) Launched App and selected to backup all versions. I actually took the tick out of the last one (Angry Birds Space) as I don't have that one, and to be honest, had never heard of it. The App will tell you anyway if you don't have it, so that you can go back and remove the tick.
3) Downloaded the App on my new phone (HTC Sensation)
4) Played the first level on each of the versions to register a score.
5) Backed Up the games on the new phone (to create the same Backup folder)
6) Connected both phones to my PC via USB on Disk Drive mode
7) Copied (and replaced) the files from the angry_birds_backup folder on the old phone to the same location on the new phone. The files are created as LUA files.
8) Disconnected my new phone from my PC
9) Launched the App on my new phone and selected the restore ensuring the ticks were in the same 3 versions.
It only took seconds, and i suppose my only bad point (I am harsh! lol) was that there was no confirmation and I like to know that things have completed successfully!
However... I loaded up Angry Birds and all of my scores were back including the golden eggs.
I preferred this, as the other methods that I had seen seemed a bit confusing for me, so I was impressed when i came across this App.
Hope this helps other people too.