Although some scientist do not consider this a true species of it's own but rather a sub species of now homo sapiens that lived between 30,000 and 40,000 years ago. I found many differences in homo sapiens and homo neanderthalensis that would indicate they they were very different. They differ in DNA by .3% for starters. Remains and tools used by neanderthalensis are found in western Europe and span to Asia. Fossils have been used to recreate these neanderthalensis and has found that they had a bigger build than modern homo sapiens. With larger cranial capacities it is believed that they had bigger brains than homo sapiens as well. Some genetic studies have even suggested that they on average had light skin and red hair. The bigger brains could also account for their advance use of tools and animals bones for building houses. They lived in complex social groups and although once thought to have only eaten meat. Further analysis of a skull found cooked vegetable particles in the teeth. There are three main hypothesis for why they became extinct. The first being climate change. It is thought that the weather would get really cold and then go into periods of less cold, only to start again. This would cause the vegetation to change and the neanderthalensis simply could not keep up with the changing of the weather and vegetation. Another theory is that homo sapiens are the cause. Interbreeding with homo sapiens eventually caused the neanderthalensis species to become extinct and evolve into modern day homo sapiens. The last theory is the classic volcanic super eruption 40,000 years ago. Overall there are many differences between homo sapiens and homo neanderthalensis which can prove that they were their own species that lived with homo sapiens for a very short period.
Rozzi, F. V. R., & de Castro, J. M. B. (2004). Surprisingly rapid growth in Neanderthals. Nature, 428(6986), 936-939.
Herrera, K. J., Somarelli, J. A., Lowery, R. K., & Herrera, R. J. (2009). To what extent did Neanderthals and modern humans interact?. Biological Reviews, 84(2), 245-257.