I hear (tweets by Razib Khan , concerning Sankararaman’s talk at ASHG) that the Denisovans had substantially more genetic diversity than Neanderthals ( determined mainly by the variety seen in admixed segments). It makes sense that the Neanderthals should have low diversity: at glacial maxima, they had to retreat into small refugia. As John Hawks says, a northern population. While the Denisovans could have spent the cold times in southeast Asia and Sundaland. The largest long-term population of modern humans outside Africa was in southern Asia during glacial maxima (judging from Bayesian skyline analysis of mtDNA) .
The high level of Denisovan admixture seen in Melanesians and Philippine Negritos may also argue for plenty of Denisovans in Sundaland.
We don’t know who was in India – but since it would have a big refugium, it probably wasn’t Neanderthals.