Funny, on my Nexus 4 and Nexus 7, moving a .mp3 into "alarms", "notifications", or "ringtones" won't make them appear as sound files when in settings under "Sounds" or in the clock app under alarms. In order to have them show up, I have to use a root file explorer and navigate to a specific root folder that would be inaccessible to the average user.
Not to mention updating my ROM (CyanogenMod for example) will revert this root folder back to normal. So for people who like to run nightlies, like myself, you have to constantly be putting in these audio files into that root folder every day.
On iOS, I could simply export out a song from GarageBand and it would do all the other work automatically.
On my SGS3, I just dropped the file into the appropriate folder and I can set it as a ring tone. On my HTC Desire Z, I did need use RingDroid to set the file as a ring tone.
In comparison, when my wife switched from an Android phone to an iPhone, I had great difficulty moving her ring tone from her old Android phone to the iPhone. I had the MP3 file on her phone and my PC, but there did not appear to be any obvious way to move it to her iPhone so that she can set it as a ring tone. After hours of searching on the internet, I finally found a way to do it.
The steps seem totally convoluted to me. First I had to change some settings/options on iTunes on her PC. Then with these changes, import the sound file to iTunes. Then I had use a DOS prompt to rename the file extension after the import. After that, I could drop it into iCloud. It would then appear on her phone as an option for setting a ring tone.
I did try to use some apps, but for whatever reason they didn't work for me. I don't remember why. It just shouldn't be so complicated to use a sound file that you have as a ring tone.
That was over a year ago when my wife got her iPhone. Maybe things are simpler now. She hasn't felt the need to change her ring tone, and I didn't feel the need to go through that again.