If your question were about the -our/-or distinction, or the -re/-er distinction, it would be a real question, but with -ise/-ize there's no contest: go with the Z form, as it's accepted on both sides of the Atlanticaccepted on both sides of the Atlantic.
The International Organization for Standardization favours British spellings, and uses the -ize form. (This is known as Oxford SpellingOxford Spelling.)