I was in a similar situation last year. I had a 290X and a 1080p 60hz screen. I upgraded to the Asus MG279Q which is a 1440p freesync that go up to 90hz with freesync or 144hz without. In your case, you'd go for a g-sync screen, obviously.
So, to start answering your questions, yes, going from 1080p to 1440p is a nice step up. More over, going from 60 to 90hz makes a big difference. Going from 90 to 144hz is noticeable to me, but less so. Going from a static refresh rate to a variable refresh rate made a big difference to me. I always run vsync on because I can't stand screen tearing. On a static 60hz screen, 60fps looks very smooth, but falling to 59 causes stutter. With variable refresh rate, 45-50 still looks very smooth and really, anything above 30 is perfectly payable, if not optimal.
To summarize that, going from 1080p 60hz to a 1440p g-sync with 90+hz should feel like a big upgrade in all respects. 4k on the other hand, might be too expensive in terms of performance even if you get one with g-sync. Do not buy a non-gsync 4k monitor for gaming, period.
I recently got a Fury for various reasons and just yesterday got my hands on a Samsung CF791. I'll make a thread and post my thoughts after I've spent some time with it. I can at least say that 3440x1440 kicks ass and didn't seem to slow down my Fury all that bad compair to 2560x1440. (The CF791 is freesync with a wide enough range to enable LFC, otherwise it would be a poor experience.) so that said, you should also consider one of the g-sync 3440x1440 100hz panels. They expensive, but also awesome.
EDIT: I just went back and realized you said your current screen is 144hz and not 60. If it's NOT g-sync, then I think you'll find that a 1440p WITH g-sync should look at least as smooth subjectively, even though you'll be getting a lower frame rate in the same situation than with your 1080p. Everything else I said still stands.