Fitbit now supports Galaxy S4 syncing, but not with S Health
Fitbit has had a pretty slow rollout to Android devices, because Google's operating system doesn't natively support Bluetooth 4.0. So, Fitbit has to perform custom development for every Android device that it adds to its support list. Fitbit assumes this development process will become easier once Google releases the next version of Android, which will have native Bluetooth 4.0 support. Then, it would be much easier to develop one version that works across devices, and leave it to manufacturers to actually get devices updated.
Of course, since the Samsung Galaxy S II, III, S4, and Note II are the only Android phones on the supported devices list, statistically that would mean quite a lot of people have supported devices anyway. If you do have a supported device, and want to get the update, Fitbit is available for free in Google Play (Fitbit hardware sold separately.)