On the combat side, the problem, I think, dates back to the original Elite. In that, the enemy ships were technically inferior: far smaller shields, rarely carried ECM, etc. - but they usually came in wings of 2-4 and sometimes bigger.
In FE2/FFE, again, the enemy ships were much less well-equipped than the player ship could be, and had terrible AI on top of that. They, again, often came in large wings.
In Elite Dangerous this pattern continues to an extent but:
- the player ship, unlike Elite, does not have intrinsic advantages over NPCs
- the player ship, unlike FE2/FFE, does not generally have much better outfitting decisions, or at least has to compromise to get them (therefore with a trade/exploration build, before engineering is taken into account, the NPCs are likely tougher than the player ships, at least on paper)
- the NPC AI is much more effective than previously
- running away from or entirely evading a fight with an NPC is much easier
So you end up with a situation where a 1v1 NPC fight is relatively straightforward in most cases provided you have weapons and shields yourself ... but a 2v1 or 3v1 fight requires a much better ship and pilot. With engineering and a decent build, sure, the wing assassination missions (6v1 or so) can be done solo, or a CZ can be a relaxing half-hour.
Ultimately I don't think it's a "PvP" versus "PvE" issue so much as a reflection of the giant disparity in power between a high-end engineered combat ship and a more generic multirole - my FDL can solo wing assassinations ... my trade/exploration Python can take on any single NPC but not two high-ranked ones at once ... my lounging-around Cobra largely runs away from fights.
More optional scenarios with high-end engineered NPCs and/or large NPC wings would be good. But I think that's all that can be done.
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On the actual "PvP" versus "PvE" side, I agree with those who say that motivations is the main difference. PvPers want to fight something. PvEers ... vary a lot in how much they want to fight, from the people who solo wing assassination missions, to the people who find all NPC attacks an unwanted interference - note that while "PvPers attacking PvEers for an invalid reason" is a common complaint on these forums, "NPCs attacking Players for an invalid reason" does come up occasionally.
Again, more high-end optional NPC scenarios would help for the PvEers who want some more challenges and PvPers who can't find a fight right now.
(Note: optional doesn't have to mean USS-based: I'd quite like Elite-ranked courier/trade missions to have tougher opposition than they currently do show up to try to stop you - in exchange for higher pay)