First off, you must understand, as a soldier, I see everything from a military point of view (rim fire kits, and parts are not an issue for me).
As far as I am concerned the Uzi is a clunky old 'SMG', and the MP5 beats it hands down, firing from a closed bolt, higher rate of fire, and the safety is more 'ergonomic' than the Uzi. The stock is also easier to extend, and more solid.
I have fired both, and I am familiar with them both a great deal, but the MP5 wins! In short, I'd rather have my soldiers armed with MP5s than Uzis.
As for the Uzi, it it a true SMG, open bolt firing, simple in design, and strips fast, and has won its place in SMG fame. Its a truely great weapon its own right. I see the MP5 as a mini 'assualt rifle', with better sights, and in general much more friendlier to use.