As far as I know there are absolutely no benefits to using anything other than Eizo’s own ColorNavigator when building profiles for an Eizo CG screen. Perhaps some may say things like the flare control (which I’ve not bothered to try yet) or some other (somewhat) obscure setting which is in i1Profiler but of course, the people who manufacture some of the most highly regarded screens in the industry and some of the highest level of accuracy screens available are most definitely going to be able to profile their own screens better or more accurately than just about any other company producing profile creation software.
Remember, not only does Eizo produce some of the few screens on the market which incorporate a 3D LUT (although, unfortunately you missed out, my CG242W on the other hand, does include a 3D LUT) but they actually design and code up their very own ASIC chips. So, no other company would have any idea of the source code and designs that go into building these very important and incredibly useful parts of most CG range screens.
I also doubt very much that any app besides ColorNavigator is going to be able to program, manipulate and correct the screen’s internal LUTs and therefore, the screens final output colours for each pixel, to as high a degree of accuracy as would the Eizo software.
But having said all that, the only judge who matters one tiny bit is youself and your eyes. If you find that i1Profiler produces profiles with better colour accuracy or much smoother transitions between colours or you simply just prefer the look of the X-Rite profile, then it matters not one little bit what sort of advantages any other app might have if you have a definite preference for the X-Rite or just any non-Eizo profile.
To me, it’s kind of like asking something like: "I’ve just bought a new Ferrari but I’m wondering if I should maybe change the ECU or engine or gearbox to a (insert whatever car company you like) brand ECU/engine/gearbox. Doesn’t sound like such a wise idea, does it? I firmly believe the same holds true for any hardware calibration screen - I definitely wouldn’t be using ColorNavigator to profile my screen if I happened to own an NEC PA271 or similar. It just doesn’t stand to reason that a company which spends so many millions of R&D $$$ on thinking of, designing and finally manufacturing extremely colour accurate, professional level screens would release an inferior software product when it comes to profiling said screen. If that were the case, then how could the company in question brag about their screens if they couldn’t even extract the absolute maximum performance from their own products.
But, as I previosly mentioned, regardless of what I or anyone else ever tells you, the only one you can trust is you and your eyes because only you know exactly what you like best and if you visiion is not “perfect” (whatever that may mean) and you see some colours stronger or easier than those of another hue/frequency, and just by sheer stroke of luck, the profiling app you choose also creates a colour cast or some other anomoly which perfectly agrees with your eyesite and vision, again, it may perhaps look better on your screen in your opinion.
Finally, you should definitely consider buying an i1d3 and using that to profile your screen instead of your i1Pro. I have both devices and have previously owned a CG241W and even with an i1d2 (which was all that was available from X-Rite for a very reasonable priced colorimeter, at the time the CG241W came out and became popular), I would get more accurate profiles, better smoothness/less banding, not such harsh transitions as I would if using the i1Pro. Especially since the CG241W can create a neutral black value well below 4cdm (I think I read somewhere that if using an i1Pro with any screen it is best not to ask for a BP any darker than 4cdm as that’s when the S:N ratio of the i1Pro, when it’s measuring very dark tones, really starts to get out of hand and give some quite strange results at times). And also the i1d3 is such a very highly stable instrument, has excellent repeatability and also inter-device agreement, certainly much better than that of the i1Pro when referring to said specifications being measured in an emmisive environment. Who knows, perhaps when it comes to measuring printed samples, the i1Pro might have just as good or better performance when given the optimum conditions. But a screen is not optimally measured with an i1Pro. The original device has now definitely been surpassed by the i1d3 for emmisive measurements. I can’t comment on the newest i1Pro 2 device.