I pronounce
Alice (AL-is) &
Clarice (kla-REES) differently, and while both are pretty, I much prefer
Alice.
Alice isn't overly popular in the U.S. and will sound sweet on a child & chic on an adult. Other than it's unfortunate association with "The Silence of the Lambs,"
Clarice just sounds a bit dated to me. Wishing you the best of luck!