The main reason PvE is so different from PvP is that none of the current PvP missions require you to fit a warp scrambler to stop an NPC from warping off, at which point you fail the mission, nor do the current PvE missions require you to use certain useful PvP skills like combat probing, safespots, and breaking gate-camps.

The need to fit a point on a PvP ship necessitates very different fitting strategies from PvE ships. The need to use these other skills require very different playing strategies. If CCP wants to blur the distinction between PvP and PvE, or at least use PvE as a stepping stone toward PvP skills, they should add missions akin to these:

(1) An L1 mission where the pilot must fit a tackler ship and tackle a fast-moving NPC target--one that microwarps back and forth across the complex. One it is tackled, he must survive its drones and counter-fire long enough for slow NPC allies to appear and kill the main ship. (At higher versions, like L3, he doesn't have any NPC allies to help kill the ship--he must bring buddies or kill it himself).

(2) An L2 mission where the pilot must maneuver his unarmed stealthy ship through an artificial NPC gate-camp. Once he hops through the fake gate, he has the normal temporarily cloak, but must get away from a dozen or so NPC tacklers in position and trying to get fast locks on him.

(3) An L3 mission in which the pilot has to use combat probes to locate a single target NPC ship in deep space. The NPC ship has three randomly positioned safespots, and it warps between them every 3-5 minutes. He must scan it down and tackle it--if he engages in combat with it untackled, it warps off and creates a new three safespots to switch between.

(4) An L3 mission in which the pilot is assigned a bounty target to destroy. The L3 version is a NPC located somewhere in the same region and on the move. This mission pays a little extra cash so the pilot can use locator agents to find him. An L4 version is one in which the bounty target is an actual player with an existing bounty--but the player has extra cash in the reward from the NPC agent, since that player has -5 standings with the NPC faction for whatever reason.

(5) An L2 mission in which the pilot must scan down and enter a special wormhole in a cloaky ship. Once he enters it, he is randomly kicked out into deep nulsec. He must get out of nulsec and back into high-sec with his ship intact to gain the cash reward. An L3 version might be one in which he can only use non-cloaky ships to complete the mission.

(6) An L2 mission in which a cloaky pilot must maneuver toward and tackle a target NPC mining barge mining illegally in the midst of a crowded asteroid field--one in which the asteroids and other non-targetted NPC ships are moving back and forth. He must keep his cloak and avoid coming within 2 km of objects until he is in tackling position of the barge, then hold it for ransom and /or destroy the barge.

(7) A mission in which the pilot must not only destroy an NPC ship, he must tackle and capture escape pods emerging from them.

You get the idea.