I think the feel is going to change no matter which way it is approached but I am curious as to what would be the feel about FE2 and FEE that you would like to see maintained in E4?
For me it's flying a ship in huge, realistic universe. I too would like to see something along the lines of rehash.
Of course, gameplay focus should be shifted somewhat towards celestial bodies - more things, like missions, to do around them and more in-game incentive, to, for example flying deep into gas giant's atmosphere, looking at it's rings and moons from below and risking getting fried by superlightning or losing control due to powerful winds and turbulence.
Of course, combat could use some diversity, like more varied and specialized weapon systems (mass drivers, anti-shield weapons, system disabling EMP, pulse plasma cannons, frag cannons, fast tracking anti-fighter and anti-missile weapons, bombs carried in cargo bay used against ground targets, etc.), multiple weapon hardpoints facing the same way, specialized missile types and more missile mounts on ships (for example, let Asp mount three missiles on it's central pylon). More options in combat (like trying to disable critical systems on a large enemy ships when flying a small fighter) would also be welcome. Finally, some sort of (toggleable - as a veteran I want to be able to fire all my thrusters manually) combat manoeuvring assist for noobs (combat would, of course, remain Newtonian) would be welcome.
Of course, more lively universe, with more handmade content, more diverse missions (deploying probes in dangerous places for scientists, rescue missions, military bombardment and insertion/retrieval missions where you would be fired upon by ground units), traffic around stations, spaceports and surface settlements, as well as between all those and more diverse scenery would also be welcome.
But the core should remain the same - flying a powerful (by today's standards) ship around a realistic universe in a Newtonian fashion.