I actually prefer iOS's file management because I tend to pear down the apps I use to one per function/task. That way, instead of navigating a sometimes poorly named directory and potentially screwing with things that need to be left alone, I just open the word processing app and all my stuff is there.
The only drawback is the files being saved in that app - but iCloud takes care of music, movies, documents, spreadsheets, powerpoints, pictures and home videos. If I were to delete any of the apps that I use to edit/show any of these file types, all the data is stored/backed up automatically and I don't have to worry about it.
I find it rather funny that those who claim Android is the future get so bent out of shape because iOS doesn't display a file system UI that's existed for decades.....perhaps some evolution is in order? Maybe there's a better way? I'm not saying iOS's way is better in every instance....just that in general it seems to contradict the idea that Android is more advanced/forward-thinking.
To me, iOS's way is just easier. Instead of the ridiculous import/export commands I get with options to save everywhere but the phone's memory (which is for some reason called 'SD Card'), I simply hold-click, and save a photo from dropbox or the web. And I know that all my photos are in my camera roll and automatically synced to iCloud.
And to recall said photo - instead of navigating a file system, I simply open the app and there it is. I guess the difference lies in the fact I don't save tons of files to my phone - therefore I don't need a file system to organize it all (I also don't care to mess with system files - but that's a different argument).