My DD is Katie so i am obviously biased!
We didn't want Katherine as that was DH's ex so neither of us were keen.
We chose Katie for the birth certificate (Katie Louise) and thought she could always call herself Kate when she gets older if she prefers.
I now sometimes wish I'd done it the other way round (Kate on the birth certificate)- for example a friend of mine's DD is Rose on birth cert but Rosie as nn.
What about Caitlin- often Katie as nn too.
Some friends spell Katie's name "Katy" but i think Katie is the more common spelling.