Not sure it matters, honestly, because NN's aren't always written. When it matters is, when it gets written and then isn't pronounced the right way. I think Addie is "cuter" to look at, personally, but Addy's fine, too.
If I ever have a girl, she will be Adeline (after DH's grandma). I would say Addie, but I'm hoping she doesn't get that nickname. I love Adeline just the way it is!
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Re: nn for Adeline
We don't do a nickname, I love her name the way it is!