My Dell's monitor is HD and full RGB. It has the full gamut.
Thanks for the response, Schewe. I doubt that my results would be identical; but I should want one system to profile both! 
Since the NEC Spectraview is wide gamut, I know that it has RGB as well. Since I never use wide gamut in my workflow, I would like one solution that gives me just RGB. For this reason, I don't think that I need to use any profiling system that is Spectraview-specific.
(Most digital displays have RGB inputs.
I think you are confusing various terms.
RGB is just a colorspace and doesn't really tell you much at all. You could have a device RGB space that covers much of the visible gamut or but a tiny trace of it.
Sending 255,0,0 to one screen might make a fairly saturated red but a crazily saturated red on another screen.
Saying the full gamut is very vague since it is impossible for any three color monitor to display the full visible gamut so this could mean anything from it has a gamut similar to a near sRGB screen or to a semi-near AdobeRGB gamut or a very close to AdobeRGB and yet also greater than AdobeRGB gamut or who knows what.
You could have a wide gamut but a device that accepts say CMYK input and not RGB or vice-versa.)
Anyway one thing is that you probably do not want to use one system to handle both screens since the NEC is unusual in that it has a fancy 14bit 3D internal LUT and ONLY (in the US that is, in Europe I think you can get BasicICOlor to control it internally) Spectraview II can calibrate it internally which is something that you really, really want to take advantage of. SV II won't work on your non-NEC screen.
So either you give up much of what you paid for when you got the NEC or you use two different programs (or order BasicIcolor or whatever it is called and inform it that you don't live in the US, I tried an early version a good while back and I didn't really care for the profiles it made for non-NEC screen so not sure this does a lot for you although I think they have changed it since then so who knows now and as for how it handles the NEC some say it's not worth the time it takes and that many probes are less linear in response than the NEC PA series is so you end up wasting time and perhaps even getting a worse or no better profile for it, to be fair, some say it does give a better result by measuring many points up and down the scale instead of just one, who knows).
You NEC i1D2 won't have any special calibration files for use with the HP screen and since their basic off the shelf calibration tends to be all over the place and that laptop apparently has either white LED backlight or perhaps an RGB LED backlight it might slightly or particularly throw that probe off, respectively. And if by RGB and full gamut you mean it's wide gamut then it would surely not work well at all with that puck.
If the Dell is white LED backlit and you have a decent copy of the i1D2 it might work out ok, luck of the draw, and then you can use it with whatever software you want just about since most programs support it.
An i1 Display Pro might be the best overall bet though. You'd have to the the xrite software with it for now for the HP screen until other software starts to support it. You could also use it with your NEC screen with SV II software and sell the current puck. It seems to read many different screen types (assuming the software knows which internal profile to use) very well and there are early, tentative signs that it may be among the most accurate pucks on average without going to like $2500+.
(If the Dell is not wide gamut (and even if it is if it comes from LED backlights instead of CCFL you might have the same issue anyway) then a side-by-side 100% visual match would be especially tricky due to metamerism issues and how the eye interacts with the very different spectral spikes of the primaries on the two screen types, plus it won't make use of a 3D LUT and most profilers can only correct saturation trackings on so on so well. You'd need color management that ran on spectral distributions and a $$$$$ spectro (like way over $10,000 the $900 spectros probably read too wide bands but maybe they could work, maybe, especially with special software and special tricky reads of raw input processed painstakingly) to measure them but I don't believe the former exists outside of the lab at this point and the latter as I said is $$$$$$$$$$$$$$$.)
