I don't really want to root either phone. But if I absolutely had to, I could root the HTC Legend, but definitely not the Samsung Galaxy S3.
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marked as duplicate by t0mm13b, Izzy, Liam W, GAThrawn, Ryan Conrad Jan 24 at 3:44
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
As long as none of the devices runs JellyBean (Android 4.1 and up), and it's just about those Angry Birds (as the comments suggest), take a look at AngryBirds Backup:
As the screenshot shows, the app supports a variety of the AngryBirds games (I don't know if it's complete, as I'm no "gamer", but it looks pretty much). So use this app to backup your AngryBirds data from the old phone to SD, copy the data to the SD card of the new phone, and use the very same app to restore them there.