In "The Flash" Season 2 Episode 6, Zoom hits Barry 700 times and then parades him around Central City. When Zoom killed everyone at Jitters, he simply broke their necks. Why would Zoom waste time and energy pulverizing Barry when he could have just broken his neck?
Note: this is more a comment on Jack B Nimble's answer, but I write it as an answer due to spoilers.
As said in the other answer, not only
Zoom wants to steal the speed of spedsters from other universes, to be the fastest spedsters of the multi-verse
but he also needs Barry and team Flash to
restore his body damaged by a problematic early version of the Velocity serum.
In the show, Jay Garrick
is actually Zoom infiltrating team Flash to get the team's help to create the Velocity serum. He is losing his powers (life too?) and is finally saved by the Velocity 9 created by Caitlin.