First of all, human species dont exist bevause Humans are a species: ours.
Second, call our species HUMANS, not homo sapiens.
Third, Neanderthals are more violent and aggresive than Humans, because:
-Neanderthals have a more muscular body, evolved for combat and hunting.
-Neanderthals where carnivores, unlike humans who are omnivores.
-Neanderthals where anti social, xenophobic and territorial isolasionists. As a result they lived in tiny groups and hated strangers.
-Neanderthals where masculine and used extreme hunting methods.
-The Neanderthal genome was found to cause humans to become more aggresive and depressed. Europeans being the biggest example.
-Neanderthals where promiscous and competitve for females.
-Neanderthals killed their prey on hand to hand combat, being fanatics of physical aggresion.
-Male neanderthals r@ped female humans, kidnapping them using their strenght to kidnap them and fight off members of their tribes.
Fourth, the aggression levels of a species depend on several factors like social structures, brain structure, behavioural traits, adaptations, etc. Our species is less aggresive than Neanders because we are more social and more designed to social than to hunt.