I think Browser Sync waits for the browser to complete the navigation. Page sync for the entire page to get loaded. I feel at times there might be instances, when the page might not get loaded completely, though the browser might complete its navigation. In those specific cases these might differ, but essentially they both do the same job.
U can use wait property/wait to halt/wait for a specific element on the page to get loaded/enabled etc.
U could also set the Browser navigation Timeout in the settings dialog.
Also check for Page load time in options dialog, i mean u can configure the same.
Also check the Object Synchronization time out in settings dialog.