Windows PC user here, and several years ago I got sick of trying to match colors, and bought a Spyder 3 (used then) on ebay, and followed the instructions.
I have a pretty good Dell HD monitor, and I use my gear for Photoshop, and was trying to get results that matched my Epson printer. This was successful - I calibrated my old Win 7 machine, and it has not drifted one little bit. My addition was to scan an x-rite Color Checker card, which actually cost a tad more than the Spyder, and incorporate the scan into a test print file that I run every week, to keep the printer exercised and unclogged. Then I hang the test print on a magnetic board above and behind the monitor, along with the most recent previous print, for visual comparison. These prints are lit with a Phillips 5k LED outdoor flood, (high CRI) controlled by a potentiometer to adjust the light level to “match”, as closely as possible, the output of the monitor, which has already been color managed by the Spyder. I had been doing this for a year or two before I finally thought to save a print for far future reference - just looked, it’s from Sept 2017, and it matches the print I ran a couple of days ago, and, no surprise to me, they match the monitor. Neither the monitor nor the printer have drifted in all these years.
Paint in my computer room isn’t perfect, a light beige, but for Ps work the room is darkened with a blackout roller blind. Your monitors are prob side by side, and you have them slightly angled to meet your eyes as you turn your head? Incident light in your space will fall differently on them, and that can introduce a different color cast to each. Darken that room.
So, you have choices as to the quality (price) of the adjusting equipment you apply to your monitors; I like my Spyder, and with the Color Checker, you might spend a hundred bucks. If you’re not printing you can just hold the Color Checker up for a visual, but being able to adjust the intensity of light falling on the card is desirable.
Key here is a better monitor than you might find at Walmart. My HD Dell is far more responsive to calibration than any low-end thing, some of which won’t adjust very far at all.
Sounds like you have monitor quality cornered.
I wasn’t sure if tou were going to print, or if mis-matched screens bugged you. You should be able to co-ordinate two good screens with calibration. And before someone chimes in with “you can’t match a display (projected light) with a print (reflected light)”, I know, I know. But you can get as close as damnit with the right quality and intensity of light on your print. Really the closeness of the match is just fine, especially since you probably will have little or no control over final print placement and hour-to-hour lighting.
Dan