And it likely was not very pretty.
Actually, it may have been rather unremarkable.
I read a statistical observation by someone, who pointed out that if every time two populations encounter each other, one of them incurs a decrease in population relative to the other, it can be statistically proven (given equal reproductive rates on the part of the two species) that one of them will eventually become extinct. (It does seem sort of intuitively obvious...).
The point was that it would not have required open warfare and genocide by the Cro-Mags (damn good band, btw) of the Neanderthals - just one more dead Neanderthal per normalized time period than dead Cro-Mags, overall - a good maxim to keep in mind today, when pursuing the global extermination of Islam...