I play Tekken rather competitively and it is noticeable, however on a game like that a 2-3 frame delays is inexcusable. For something like FFXIV where the timing is probably not going to be as critical for < 1 second, if you aren't lagging connection wise, you are golden.
I know it's a long thread but there are a LOT of screenshot comparisons on many models of many sizes all the way from 19" to 60"+ so I highly recommend reading...well all of it. As much as I love my Samsung TV and it's picture for Blu-ray is amazing, Samsungs tend to have notorious high delay rates, up to 80ms. Game mode does help but not enough for the listed games.
FPS online, fighting games and some sports games with precise kick meters are very noticeable, there is no denying it. As a matter of fact, the exact reason WHY Rock Band includes a calibration is specifically for this reason and many people use that in there delay tests, along with other methods.
P.S. You got rated down because of the haters, it happens. When hard facts come out, some people get all bent out of shape; forum has been on high tension mode for obvious reasons as of late.