According to the new paper, this diversity was lower than modern day Iceland, however it had been larger before 48,000 years ago.
Love Dalén et al., Partial genetic turnover in neandertals: continuity in the east and population replacement in the west. MBE 2012. Pay per view.
Remarkably little is known about the population-level processes leading up to the extinction of the neandertal. To examine this, we use mtDNA sequences from 13 neandertal individuals, including a novel sequence from northern Spain, to examine neandertal demographic history. Our analyses indicate that recent western European neandertals (<48 kyr) constitute a tightly defined group with low mitochondrial genetic variation in comparison to both eastern and older (>48 kyr) European neandertals. Using control region sequences, Bayesian demographic simulations provide higher support for a model of population fragmentation followed by separate demographic trajectories in subpopulations over a null model of a single stable population. The most parsimonious explanation for these results is that of a population turnover in western Europe during early Marine Isotope Stage 3, predating the arrival of anatomically modern humans in the region.
I do not have access to the paper so I remain in doubt about the details, however I wonder if this genetic bottleneck or founder effect may be related to the formation of Chatelperronian culture (oldest dates (ref: direct download): Grotte du Renne since c. 52 Ka calBP, Roc de Combe since c. 49 Ka calBP). It'd be interesting to know how these Western Neanderthal individuals correlate with the cultural mosaic of the MP-UP transition period c. 50-35 Ka BP.