Hm, that’s going technical now 
(short version)
The Eizo CG2730 (main screen) is equipped with a built in device and does hardware calibration ‘automatically’, based on my custom sets of parameters in Color Navigator 7, and as I’m very happy with the results I did not experiment any further.
My Eizo L767 (extended screen) as well my notebook are both software calibrated with Quato’s ‘Silver Haze 3’ (i1 Display xx from X-Rite) and Quato’s iColorDisplay software xx.
That’s how it works since 3 years now – all set to 80 cd/m².
I’ve been ‘fighting with colour’ long time (don’t remember, when I switched from Win95 to XP).
Around 2008, I started exploring colour management more seriously (X-Rite’s ‘Color Munki Photo’ + software, 2x Eizo L767, Epson R2400 at that time).
Must have been Color Munki’s bulkiness (>> monitor calibration), the software’s limitations as well as sRGB colour space, that I decided for an upgrade and went for the hardware calibrated Quato IP262ex, bundled with Quato’s extraordinary iColorDisplay software + ‘DTP94’ from X-Rite. Later I got to know, the (regulary) hardware calibration process was done much quicker with Quato’s new ‘Silver Haze 3’ (1st generation of X-Rite’s ‘i1 Display pro’).
When my Quato went wrong, I replaced it with the hardware calibrated Eizo CG2730 + Color Navigator software. Their ‘buttons’ allow to flip instantly between 6 custom calibration targets, meanwhile my second monitor rests on sRGB, (manually approached to the main screen, when set to my standard: 5900 Kelvin, 80 cd/m², AdobeRGB) – so, no automatic display control stuff.
As I was building paper profiles with Color Munki Photo + software, I got the chance for a (second hand) X-Rite ‘DTP20 UVcut’ (commonly known as ‘Pulse’), which was sold by Quato + bundled with their extraordinary iColorPrint software. Right out of the box, their process is (was) a lot faster. In contrast, the easy to follow but stripped down Color Munki Photo software works iteratively plus the profiles can be tuned (and then are as good as with DTP20). BUT, when one likes double weight paper, better let it dry overnight before continuing.
When I replaced my computer (and changed from Win7 to Win10), I had to realize, X-Rite is not supporting my trusty DTP20 anymore (was really mad), as about the same time they had started with renewed products, also offering their i1 Studio line to beginners and enthusiasts.
This i1 Studio software *) supports my old Color Munki Photo, the new ‘i1 Studio’, 'i1 Studio ‘Display’
[ see https://www.xrite.com/categories/calibration-profiling/i1studio ] … long way to go.
have fun, Wolfgang
*) set up to check Mike’s monitor calibration process