The sheer simplicity of the Uzi is it's advantage. I can break my Uzi into it's component parts in under a minute with no tools. I can change a broken part or a bulged/shot out/squibbed barrel in seconds.
The Uzi is like the 4x4 truck of the subgun world whereas the MP5 is like the German luxury car.
I would take my Uzi places where I would leave a borrowed MP behind.
Stopping power: The power some guns have to make you stop what you are doing and get your wallet out.