Ringback Tones are not stored directly on your device so you will still have them after a phone change. For Ringtones I would also suggest the media retrieval.
I was in the same situation when my kids surprised me with a new phone - and I had just purchased a couple of ringtones!! I could see them on the retrieval list but there was no where to click or check although it appeared it was SUPPOSED to work that way.
I had to call customer service, explain the situation, go "rebuy" and "redownload" the ringtones, and they credited my account for the purchase price and the download time, as we don't have a data plan. Kind of a pain to do all that, but it worked!