I've played and enjoyed them which is why I was curious - and they are very turn based tactical combat, much like X-Com. Except easier.
I've finally caught up on Shadowrun Returns during the holidays.
The game is borrowing elements from SR2 and SR3, and some concepts of it such as using cover or different fire modes, but overall it has little to do with the P&P rules of any edition. The P&P system has no HP, no action point mechanic, no abilities with cool-down, no special abilities unlocked at certain attribute/skill tresholds, summoning works completely different, hacking works completely different, rigging drones works completely different... None of the editions comes even close to the Harebrained system.
The module structure is also very different from the normal Shadowrun module.
Harebrained plays more like a conventional dungeon module, expects you to go from room to room, slay a conveniently sized encounter and then rinse and repeat.
The P&P generally expects you to do legwork and scouting, advance unseen and undetected as far as possible, and only get into open combat once it becomes unavoidable (and then to fulfill the objective ASAP and bolt out and flee as fast as possible before alarmed reinforcements, drones, FRTs, SWATs and the like overwhelm the runner team). - The ground level of the infiltration of the UB compound in the last mission comes closest to a typical SR module, only switch back to hack&slash mode in the underground levels the latest.
(SR Returns also felt more like an extended tutorial to the game mechanics, rather than like a complete CRPG.)