if you want to take moving subject, it would be better to have high ISO noise control rather than OIS. so i recommand the fuji in this case. but if you are talking about zoo animal, both ain't good as their zoom aren't far
go for the fx01, you will learn to appreciate the 28mm especially for such shots. further more i think the fx01 have a slightly better metering than the fuji, this could simply mean lesser tuning to get correct exposure.
if you are getting fuji, f20 and f30 are almost the same except f20 doesn't have manual mode and some are not as useful features are a little crippled