In the comics, the outcome of their battles varies. Sometimes Venom emerges victorious and kills Carnage, but there are also instances where Carnage escapes or the fight ends inconclusively.
The back story of Carnage and Venom is quite complex. Both originated from the symbiote species. Venom was the first to bond with a human host, and Carnage emerged as a more violent and unstable offshoot.
Sure, Carnage is often depicted as slinging in the comics. This is a common trait used to showcase his aggressive and chaotic nature. His movements and attacks involve a lot of slinging to cause chaos and destruction.