I think we can have a vague idea of that if we just look at the mainly Neolithic Near Eastern-derived populations of West Asia, Southwest Asia and North Africa, as well as some remote regions that are overwhelmingly EEF (ANF + WHG) even today, like some parts of Sardinia. No, I don't think they'd be significantly less warlike, less patriarchal and more egalitarian than the Indo-European societies. Neolithic farming societies were also usually strongly kin-based and had a communal (clan-based or tribe-based) property of the land which would inevitably cause many conflicts especially in times of scarcity.
I think we'd see different cultural and social organizations, but with the development of fully established states and complex economies they'd vie for wealth, power and dominance just as much as other peoples, especially because they were mainly farming societies, which are noticeably associated with increased patriarchal structures and significant income inequality (especially access to land) in most places where advanced farming civilizations happened.
On the other hand, I think they'd probably have developed urban communities and organized state institutions earlier than the Indo-European-derived societies of Northern & Central Europe (in Southern Europe, it's clear there was a huge influence from the local Neolithic societies and also from civilizations on the other side of the Mediterranean). Until horses were adopted by them much later than they in fact did, those non-IE Europeans would be less mobile and more attached to their territories, possibly stimulating the earlier development of large-scale agriculture and permanent building.
