Yeah, on last informations I add the "pros" of Fast monitors (blurbuster) agreed (and also the pro fps games players) that for theses kind of games (where faster the monitor the better), you do not want gsync enabled. that maybe not new for you, i think the reason is sometimes somehow gsync will miss a frame to be more consistent, frame that theoretically (and apparently in practice too) could have helped you win.
I don't know if it still the case for gsync 240hz, you should really go read about it in blurbuster forums and after a bit of reading ask nicely what you didn't understood.
about the input lag thing, i was one of the guy defending that on the internet, simply because i red a ton of reviews, and people like the tft central guy and other made professional tests of input lag, and (not at all a question of frame like the first answer said), they found out with their settings, that input lag (and input lag only, 240hz is still faster and smoother in an other way) was a bit longer on theses news 240hz tn panels they tested.
it could (but shouldn't) be a miss setting or something, but i would actually not be amazed it's not.
input lag, and other measurements of the "fastness" of a monitor have also a lot to do (other than the pixels themselves abilities to switch from a color to an other the shorter, just for information the 1ms is for GtG but for other color switch for now on the market there is no monitor that can make better than 5ms, it's characteristic itself of the TN film and nothing better is available for now) with the little motherboard of the monitor and how it communicate with the panel.
If i don't mistake theses motherboard are not made by Panel manufactures, but buy reseller (i.e. asus, benq, acer etc..). So they may not achieve the best as possible for exemple for precisely input lag. Some motherboard may communicate the info from the gpu fastest or in a more efficient way than other. Or the tester missed a setting, while it's possible I also doubt it.
TL;DR : Go to see on blurbuster forums. And for the passionate gamer that want / are willing to wait before buying a 240hz monitor, I think there is a windows of clarification about all theses stuff that will be fully available in less that one year. Recently MSI announced for this summer the first "0.5ms GtG" 240hz panel. So there is improvement (or seems to) made and maybe it's worth to wait a little to see who is the fastest of the fastest.
For now I would theoreticaly if I was in your position trust Zowie by BenQ that somehow are the first choice of all competitive gamers, and that is the brand that shown the best result about input lag of all times on testers list.
But again maybe now the 240hz technology is too fresh to provide all the answers. Go see blurbuster
Edit : after a bit of reading, about gsync nothing changed with 240hz compared to 144hz. 240hz without gsync it still faster somehow, simply because if all is maxed out (unlimited fps), the monitor can start to draw the next frame on top on the first frame.
So you may see (let's say in a fps game, same comparaison can be done with rocket league) first the head or the feets of an enemy with gsync off, but the image can be a bit "blurry of some sort". Gsync will eliminate this problem, so you'll experience less "microsluttering/micro tearing", image will be more clear and maybe even the experience feel smoother, but for example let's say in csgo if someone is fast picking from a corner you have in view, the guy with gsync off can have some miliseconds advantages on the guy with gsync on. i think it's why 0 pro's use gsync and so 240hz doesn't change anything to this.
But if you play other games, you really should consider gsync advantage on lower fps.