Presumably you mean homo sapiens, because Neanderthals were also humans. I have no idea whether Neanderthals would qualify as possessing behavioural modernity, but because homo sapiens out-performed Neanderthals, presumably because of their limited ability to adapt to changing conditions in Europe, it would seem a little odd to suggest that they should be more technologically advanced.
For that matter, depending on how you define stone tools, you have three major increases in technology during the Olduwan (2.5 Ga), Acheulian (1.5 Ga) and Mousterian (200 Ma) eras, and depending on from when you date the emergence of Neanderthal man, all three advances may predate them.