Tommy Gun is immensly helpful during the main story, but u get it really late in the game. This DLC lets u have it from the get go, and kinda turns otherwise hard beginning into piece of cake - provided u have resources to craft ammunition that is.
Is it worth the full price? That only depends on how much u struggle with fighting in this game. If it's a breeze - u don't need it at all, just wait for standard Thompson in story.

P. S. As far as I know, Chicago Organ Grinder is not in any way better than normal version.