Good point, what I've bolded. This is a very good question. I know some debate rages over this in scientific circles. I did a quickie search on Google, and here's a good article that specifically addresses this issue:
Did the Neanderthals have Language?
I've cut and pasted the relevant part of the paper. Haven't had time to read the paper. After all, I'm at work. :-)
Also trying to improve my HTML skills, so bear with me.
This discussion has so far given an explanation for how language is acquired by children, an explanation of how language could have evolved and forced the increase in cranial capacity, and the consequences of brain expansion due to language on cranial morphology. This paper will now attempt to argue for a Neanderthal capacity for symbolic language, and a probability that some degree of symbolic language was present using the evidence presented throughout this paper.
The ancestors of Neanderthals were present in Europe by at least 800,000 B.P. (Kunzig 1997: 96; Lahr and Foley 1998: 157), and remained relatively isolated from African populations over time (Stringer & Gamble 1993: 193). Over this period, the Neanderthals reacted to selection pressures to adapt to the cold environment according to Allen and Bergman’s Rules (Holliday 1997). Neanderthals carried more weight than modern humans (Bergman’s Rule), and while the exact mass of Neanderthals is not known precisely, since all primates have a skeleton that weighs 6-7% of their body mass, Neanderthals should be expected to have more robust bones than modern humans. Thus, an increase in brain size may have had less of an effect on decreasing the face, leaving them with a more prognathic face than modern humans. Regardless of the robustness of the Neanderthal crania, the internal size of the palatal cavity is not so much larger than modern humans that the position of the Larynx would be significantly different. Hence, Neanderthals were likely to have had the capacity for speech in terms of structural and motor characteristics.
The capacity for symbolic thought is harder to quantify. The fact that the Neanderthals made complex tools, made decorative body ornaments, may have took care of their elderly, may have buried their dead, etc., seems to indicate that there was symbolic thought processes occurring in their brains. The real question is whether symbolic linguistic communication had replaced more animalistic forms of communication. Decorating one’s body and caring for another of one’s species well being may indicate a sense of self and other, but they cannot prove whether symbolic communication went on between individuals; many animals have been shown to have a concept of “self” (Griffin 1992: 249), and animals like elephants will try to help an injured elephant, indicating an awareness of "other", and yet there is no symbolic communication. Although Neanderthal had slightly larger brains than modern humans, when scaled to body mass they have slightly smaller brains. At the very least, this would seem to indicate that either Neanderthals had been using symbolic language for a shorter period of time than the stock that led to modern humans, or that there was less intensive selection pressure for cortical capacity due to smaller social size or less social communication. Thus, if Neanderthals did have symbolic intercommunication as well as symbolic intracommunication, it was likely to be less complex than modern language in some respect, if only in capacity for vocabulary.
The key to the Homo sapiens replacement of Neanderthals may have been sheer weight of numbers. If humans had a larger social group size, then they would have had more intensive selection for language, giving them larger available cortical area to use for conditional learning, and a higher reproductive success since larger groups would afford more chances for mating and give a greater chance of offspring survival. If Neanderthals were in smaller, more isolated populations, then their reproductive success would be lower than that of humans, and they would have developed less available cortical area for conditional learning. In addition, if humans brought tropical diseases with them, many Neanderthals may have died from disease quickly, allowing humans to replace them easily. Neanderthals may or may not have had symbolic language similar to modern language, but they did have the capacity for learning and using modern language.
Some of the important stuff is bolded. All very interesting.