It is definitely possible to see the differences, but they are in the relative margins. I routinely shoot an FX and a DX camera at some events, and most of the time one would be very hard pressed to tell the difference between them. I'd post a couple of examples but I'm traveling and don't have access to my archives. However, in some other cases, it's apparent which is which. I have some B&Ws taken at night, and the ones from the FX camera are, as one viewer put it, just leaping off the page; the ones from the DX camera are just not as nice in contrast and dynamic range. Since in that case I was also using both an FX and a DX (and with physically the same lenses), I'd say that the difference was mostly if not completely down to the camera. Now that does NOT necessarily mean FX or DX - my cameras are from two different generations, and things clearly did advance all 'round from the D2x to the D3. But one can see the differences there.
The question is often posed as you have - FX vs DX - but just as an example, I am pretty sure that a D7100 will look better than a D3 in most regards other than maybe in high ISO and extreme AF performance. Yes, in that case, I think a DX outperforms FX. OMG, how heretical! I would like to replace my DX camera; not because I want to "go all FX" but simply because I want a more modern camera in the larger body style that likely will not see another DX sensor.
> replacing my DX lenses adds a lot of additional cost.
No kidding. I had it relatively easy since I had a whole stable of 35mm film lenses, and by accident I had picked up an FX ultra-wide early in my digital career. (Ie the Sigma 12-24 FX, which was my original choice for wide angle on DX.) My only real DX losses were an all-around 18-200VR and a fisheye. But for many people, the FX body is just the tip of the iceberg. At the time I bought FX, it was the only way to get a decent ISO 6400 and it was before Sigma came out with the DX circular fisheye. Now there are many more choices, and spending FX money seems relatively less necessary, even as the market has clearly voted that FX "is superior."
_____ Brian... a bicoastal Nikonian and Team Member
My gallery is online. Comments and critique welcomed any time!