Many sources say that humans are 99.5 to 99.9 percent the same.
Also some sources state that some humans have 3.4% Neanderthal DNA and some don't share those genes.
Why is that?
3% and 99.9% are from different calculation method.
20% (a rough estimation, might be wrong) of neanderthal DNA survived in the modern human genome, but it is 'diluted' by the human population, which lead to 2 percent of neanderthal DNA in each human genome. This is the number 3%.
But how can we know it's neanderthal DNA?
If DNA fragment contains several neanderthal special SNP (single-nucleotide polymorphism), we will treat it as neanderthal DNA. (Based on linkage disequilibrium, the inference is reasonable.) The fragment might of tens of thousands nucleotides, but the difference are just one or two base.
But when we compare two human, we calculate the difference at nucleotides level, rather than DNA fragment. This is the number 99.9% come from.
If we have the complete genome of neanderthal and human, by comparing them at base level, the similarity might be great than 99%, I suppose.