Not all of the work has been published yet; Razib Khan has been tweeting some recent posters/presentations on more work on Neanderthal purging and uneven inheritance suggesting that the Neanderthal variants were especially harmful for some things like the central nervous system ( https://twitter.com/jgschraiber/status/881995470515687425 https://twitter.com/StoneLab_ASU/status/881994861158813697 https://twitter.com/jgschraiber/status/881995155875692544 https://twitter.com/jgschraiber/status/881994429510365186 https://twitter.com/jgschraiber/status/881993396642091009 ).
Greater genetic diversity might seem like a good thing, but there's a lot of details. Neanderthals might have been too alien for their variants to be 'compatible' with humans (not as surprising as it might sound, an interesting paper from yesterday reports that this sort of incompatibility may be responsible for as many as 95% of one project's mouse strains dying out despite all of them being interbreedable: http://genestogenomes.org/behind-the-cover-male-infertility-... ), or they may have suffered from a higher mutation load due to their small population - small populations can't select as effectively against bad mutations, so will be genetically less healthy. (This also might be part of why human mutation load was shrinking over time up until a few thousand years ago, "The Genomic Health Of Ancient Hominins" http://biorxiv.org/content/early/2017/06/02/145193 Berens et al 2017, all the new variants being slowly sorted through.)
Thus, while some Neanderthal/Denisovan variants may have been helpful to humans (like the Tibetan altitude adaptations), overall they appear to have been harmful and are disappearing.