Not sure there is a rule; seems that /i/ and /ai/ are working in free variation according to one's idiolect. One possible explanation for someone using both might be that the older pronunciation is /ai/, and is therefore used in older words (antibiotics, antifreeze), while the /i/ is taking over and gets used when "anti-" is applied in newer words (anti-Bush). Or when "anti-" is hyphenated. Just a speculation, though.
Antee-biotics, antee-freeze,antee-Blair etc (except that -ee is quite short. People here tend to make a longer 'ee' in 'antediluvian' and other words prefixed ante- )
The pronunciation 'ann-tie' is North American and it's interesting to read that even then 'anti' has two versions.
On this, there is one American pronunciation which puzzles me . It is of route. I hear both 'rout' and 'root' . Is that a local difference or a personal one? (We say 'root' )