I like
Adeline and
Ada, but not
Adeline '
Ada'. I wouldn't say the nickname is far fetched or anything but it feels a bit forced especially because
Adeline begins with an Ad-sound and
Ada with an Ay-sound. I like
Adeline and
Ada separately.
Ada is very strong, strict and no-nonsense.
Adeline is sweet and friendly and at the moment I prefer it over
Ada.
The only issue with
Adeline is its pronunciation. I have heard the ending pronounced as -line, -linn and -leen. My favorite is -leen, followed by -linn. I don't care much for the -line ending in this case.
I also really like
Aveline.