I have Angry Birds both on my iPhone and iPad.
I find it frustating that I have reached far ahead on the iPhone, but on the iPad I am still in the early levels.
Is it possible to sync my progress between the two devices?
I agree with this question and have an unfortunate answer.
The saddest part of the iOS line is that iTunes does not back up CoreData / Application generated data (save games, favorites, you know, locally saved data). The only way this is feasible is if the application supported saving progress back to the server, and loading it back to the device next time you play. And, clearly, Angry Birds doesn't.
This is an opportunity to contact the developers about Angry Birds and ask them to implement a server-side store of your progress, in ADDITION to the local data.
This answer is 50% wrong. A server side store would be great, and iTunes doesn't back up Application generated data, but you CAN pull saved files out with some finagling.
I just tried http://www.macroplant.com/iphoneexplorer/ and it allowed me to just drag and drop my highscore file from my old iPhone (2G, jailbroken) to my new (iPhone 4, not jailbroken). Hope that works for you too!
This isn't necessarily a new answer but it aims to be more specific than the previous ones (I can't comment other answers yet).
What you need to do is get the highscores.lua file which naton refers to. If you are able to browse your iDevice's file system (using any of the many programs which do this. I used Phone Disk), then this file will be located at
[location of iDevice root]/private/var/mobile/Applications/[xxxxxxxx-xxxx-4xxx-xxxx-xxxxxxxxxxxx]/Documents/highscores.lua
That long part with x's is the UUID. It will be unique on every iDevice. If you look in all of the folders in the Applications folder, you will eventually find one that contains the AngryBirds.app file. Inside that same folder is where the Documents folder that holds your highscores.lua file is located.
Now that you have the file containing all of your progress (almost. I'll get to that) you have to dig through all of those UUID named folders on the destination iDevice until you find the one containing AngryBirds.app. Once you've found it, you can overwrite the highscores.lua file in its Documents folder.
Here's where I ran into a problem. Apparently, Phone Disk doesn't copy permissions correctly and neither do some other programs. I suspect this would happen with any of the Windows programs, though it happened to me in OS X. So you'll need to make sure that highscores.lua is able to be executed by the mobile user. I connected to my iDevice through SSH, and navigated to the Documents folder inside the AngryBirds folder. I issued the following two commands as root:
chown mobile:mobile highscores.lua
chmod 644 highscores.lua
Before I had changed the permissions, Angry Birds would crash every time I played a level and got a new high score.
Finally, when I say almost all of your progress, it's because when I did this, there was a level that only had 1 star when I had previously had 3 stars. Also, some of my golden eggs were missing. They came back after I replayed the levels that they existed in. Some of the achievements were missing, too. Anyone want to comment if this is the same experience they had?
And one last thing, I remember reading somewhere that the highscores.lua file is compatible with the Mac OS version of Angry Birds. I didn't feel like buying it to test it out, but please comment if you can verify this.
With my iPhone 4s, i managed to back up the levels thanks to Birds Scores - it really works. All you deal with is just highscores.lua and settings.lua. The app is 4m Softorino. I don't want to sound promoting, though. I will test it with my iPad 3.