Don't use the Spyder, it works on the video card instead of talking to the monitor itself, which is vastly superior for a number of reasons. Both those models can be hardware calibrated with dedicated software, and that's something you should take advantage of. For the NEC you'd have to buy Spectraview II software separately (the US, not the Euro version). If the Eizo comes with EasyPix included, you're in business.
I've used an NEC P232, and it's an excellent monitor indeed - except one problem: there is a very pronounced off-angle blue/white glow to the blacks, which is quite disturbing. This is in fact a common phenomenon known as "IPS white glow", inherent to the IPS panel technology, but I've never seen it quite as pronounced on other IPS models. Maybe it was just my copy.
If these two are similarly priced where you are (this varies around the world) - and you're determined not to exceed your budget - I'd say the Eizo EV2436 is the winner.
However, if there is one place where you should spend as much as you possibly can, it's the display. It's the most critical piece of hardware you have, and it will have direct impact on your work like no other piece of equipment (except camera and lens, obviously).