But in the biology of animals, speciation is determined by whether two recognizeably distinct populations can and will interbreed. It they either can't, (because they're physically or genetically incompatible) or they still wouldn't even if they could, then we can consider them different species. We can't really know whether that was the case with Neandertals, so we can't say conclusively whether they were
Homo neanderthalensis or
Homo sapiens neanderthalensis. But the criteria for subspecies is a lot less strict, and equates to a "breed" in dogs. Each member of the subject population must share some trait with every other member of that population, and that trait must be unique to that group, not shared with any member of the alternative group. And of course the alternate group should have their own unique distinction shared amongst all of them that isn't present in any member of the subject group.
The earliest neandertals were already distinguishable from Archaic Homo sapiens. But later groups diverged much more significantly so that we may have the makings of a speciation, but we definitely already have a separate subspecies.
:
The more recent Neanderthals consistently had a stockier build, stronger deeper jaw, broader nasal cavity, and a pronounced brow ridge with no forehead to speak of. This was in common with Homo erectus, "father" to both Sapiens and Neanderthals. Both of the daughter species had larger brains than erectus, but Neanderthal brains were actually larger than ours! Although their frontal lobe may not have been as well-developed, and this may account in part for the lack of artistic expression found in Neanderthal homesites. But yes, at the very least, Neanderthals were a distinct subspecies, if not an entirely different species by the time they went extinct.