This is a tough one. The EIZO can be a nice monitor and it is completely unique, but the quality control is really bad. It's always something of a lottery with inter-unit variation on monitors these days, but your odds are pretty bad on this 'lottery'. Brushing these issues aside, as there are definitely 'good samples' out there, what you'll get from the experience really depends on your system and how you like to play your games. The EIZO relies on the strobing of its 'Turbo240' mode to compensate for some very slow pixel response times and essentially hide a lot of trailing. For Turbo240 you need to be running your games at a solid 120fps or things quickly go downhill from a visual fluidity perspective.
The BenQ model (XL2420T or XL2411T) is definitely responsive. It has lower input lag and much faster pixel response times than the EIZO. It also has a higher (144Hz) native refresh rate - don't be fooled by '240Hz', this is just interpolation and part of how Turbo240 works. Unlike the EIZO the BenQ doesn't have a native strobe mode so it actually has somewhat more motion blur. The only exception to this is some sluggish pixel transitions on the EIZO aside which will crop up from time to time that even the strobing can't hide. Unlike the FG2421 there isn't such a huge drop off in visual fluidity as the frame rate drops even slightly below the refresh rate. It's still best to be matching frame rate to refresh rate if possible but the stuttering is nowhere near as pronounced.
A better comparison would actually be with the upcoming BenQ XL2420Z, due out in the UK in March, which has a native strobe backlight mode. I'm also hoping that it might (just might) offer slightly more richness after tweaking than the BenQ. You just wont' get the same contrast performance as on a good FG2421 or your Sony Bravia on these TN panels no matter how well they're set up. I'm not going to pretend the image quality can really compare. But some gamers really do want the lowest possible latency and don't want any 'trailing' from the occasional sluggish transition that the Turbo240 magic can't entirely hide. For them the BenQ is a better choice. Particularly the XL2420Z, perhaps, which I'll be reviewing very shortly.