Frankly, 6800 is substantially better than 6700. The thing is what you are trying to do. If your current PC is running 4440, there's literally no point going for i7, because you will not be able to get anything reasonably new and strong, because your motherboard wouldn't fit the new-ish generations - so your only option would be going with i7 of the same generation and that would make 0 difference and be shit.
On the other hand, I am not sure, but have a feeling 4440 wouldn't be able to squeeze out all the juice from 6800, so kinda pointless too. I think, in theory, 4440 with 6700 should be able to give you 1440p, but keep in mind that it obviously won't be all Highs etc., but think you should get reasonable FPS within Mid range, which trust me, is often more than enough to enjoy the games.
So long story short, 4440 with 6700 is a way to go in my opinion, but keep in mind that it won't be a jaw-dropping rig, it will be good enough till the moment you can afford a better one. 4440, 6700 and 16GB RAM can only go a certain way.
Upgrading 4440 for old i7 is pointless, unless you go for newer i7 and it would require replacing half of the PC. Upgrading to 6800 with the 4440 rig would be a bit of a waste.
The go to strat here would be getting 6700, start saving up just a tiny bit every month for two years and then going with something like 13600k and 3080 - trust me, in two years it will be very very affordable as new gen will come out. Good luck!