I believe if you use Smart Switch and do a full backup that should work. I have done backups of my S5 and it kept the blocked numbers when I had to do the factory reset to my phone.
Sorry about the last post not sure where the post was in I thought it was in S5 but guess I was wrong. Obviously the smart switch will not help you with this problem.
Great question, so let's get right to it. Generally, a blocked call list is saved to the phone itself. However, keeping the same AppleID on the phone would ensure that as many compatible settings are transferred over into the new device as possible. I have had an iPhone 5s, using iOS 8.4, transfer my own blocked numbers from the previous iPhone and all I did was share the same AppleID between them. As with anything, make sure your content is showing up in the new phone before erasing the previous one.
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