Have played Elite since Day 1 release; bought SC about 2 months ago.
(IMO) The flight model isn't bad; it's simply different than Elite. It feels a bit more like Xwing, or in some ways Descent. To me, it does not feel like I'm flying a debug camera. Once you have your controls mapped well, it feels quite nice actually. I get more of a sense of full-motion 3-axis movement, than with Elite - which feels (and is controlled) more like an airplane. Again, nothing wrong with the airplane flight model. Elite uses a pure roll+pitch to change direction; SC allows that if you like, but SC hasn't nerf Yaw to the point it can almost be ignored. Yaw, in SC, is just as utilized as Pitch and Roll. Thrusters (up/down left/right) are a bit stronger and more responsive than in Elite as well. I use them alot more in SC than in Elite for lateral moves, or combining with a roll or yaw.
Thus, Ship Combat feels different. In the starter ship I have, there are no gimbals. No "autobot weapon tracking". You have to paint your target, and stay there, if you want to get a hit. I like that quite a bit; it brings skill back into dogfighting, vs Turrets & Gimbals.
Speaking of Turrets - no, SC combat doesn't feel like "turrets in space" ... well, no more than it does in Elite, when 2 Condas square off nose-to-nose and pitch around each other @ 1400 meters for 5 minutes.
Damage modeling on ships is definitely further along than Elite. You don't target subsystems as easily as in Elite, but it's more engaging in terms of... you actually see the wing fly off, for example (and it affects the ship's flight abilities). The HUD gives you feedback on where you're causing damage... it's not a chart of percentages, as in Elite (or scrolling through subsystems 1-by-1.)
Other differences:
Elite has 400 Billion systems, SC has about 12 or so locations. If the appeal of Elite to you is "fly somewhere no one has been" - nope, you won't like SC. However, if you actually enjoy "fly somewhere that other people are interacting", SC delivers. And FWIW, the "hyperspace jump" is pretty nice. It's not a loading screen; you can target a destination or just jump where ever you like. And the visual of passing by planets/etc is nifty.
The FPS aspect has promise, but it's still alpha and a bit clunky with collision/boundries. But it does add a lot to the game, being able to walk about, climb in a ship (solo or with a team of people.... your own ship, someone else's ship, or a stolen ship.) At one point I got ejected from the ship I was in, about 4K away from a station. Just to see if I could, I tried to fly all the way back just in my space suit. Took awhile, but did make it. Talk about immersive...
There aren't many missions at all. The ones that are in, do work well... and aren't just "deliver this thing over there" missions.
If your main thing in Elite is trading cargo for profit, you probably won't like SC right now.
If you're mostly an Explorer in Elite, you'll probably hate SC.
You need a really good PC to run it. My 7yr old HP is barely up to it. This is a big criticism people often mention, but for me it's playable - and, I know the meaning of the word "alpha".
Do I feel like I wasted $45? Hell no. I've played SC more in the past week than Elite in the past 2 months. It's alpha, it's buggy... but it's also FUN.