I also have both - I have never fired my M 11 with the stock 9 mm upper, I did shoot it with a Lage 22 kit installed - what I noticed at that time - you have to be very careful not to get your support hand near the muzzle, which is a concern if you let beginners shoot it. When I bought my M11 it came with a Lage Max 11 upper and have since purchased a Max 31 upper, red dot sights for both uppers, lots of other accessories and multiple cases of ammo, all for less than the price of an Uzi -- the Max 11 is faster to reload (with the Lage thumb mag release installed) but more mag sensitive (M 11 mags are harder to load than Uzi mags)
Uzi -- takes a touch longer to reload, new shooters have trouble with the grip safety and it is heavier than the Max 11 Mk II.
Quick change barrel on the Uzi and simplicity of field stripping make it easy to clean and to change from optics to irons -- are just some of the things I prefer on the Uzi.
All that being said - I still reach the Uzi first now days (it is my latest addition which probably has an influence) unless I want/need mag capacity then the Max 31 get the call, just got the Lage Mk II a couple of weeks ago but it does fell just as good as the Uzi
If price is a concern go with the M 11 with Lage upper (I have never dealt with a group than Richard and Jackie Lage) if you want the military history get the Uzi better yet GET BOTH