While H&K's MP5 is an acknowledged leader in the submachinegun category, used around the world by police and military, it does fire a fairly small caliber round- the 9mm Parabellum. This is great if you happen to be carrying a 9mm handgun- you have interchangeable ammunition (remember Die Hard- Bruce Willis was able to take ammo from a seized MP5 and use it for his Beretta 92 pistol).
But sometimes you might want something that packs more of a punch- and that's where the UMP-45 comes in.
Firing the .45 ACP cartridge, which is half again as heavy as the 9mm, the UMP incorporates a lot of the MP5's features, but in a much more target-stopping round. (There's also a variant that fires .40 S&W)
With more power though, there's more recoil, which meant the cyclic rate had to be dropped to only 600 rounds/minute (less spraying, more praying). The UMP can fire single shot, 2-round bursts and full auto. It features many polymer parts, reducing corrosion. It accomodates a number of attachments, from different sights to aim lights and more. There are versions that will accept silencers. And its straight-magazine holds 25 rounds.
For the Stone Soldiers, the UMP offers superior stopping power for light targets, like parahumans. Weight and recoil aren't much of a consideration for the stone soldiers, but as they are trained to be accurate, the reduced cyclic rate is not a factor. Additionally, the .45 ACP round is interchangeable with that used in their Mk23, Mod 0 sidearms.
All in all, an effective weapon, introduced into the series in Book #6, Armageddon Z.