I can't figure out why the Atkinson profiles get as much attention as they do.
There's really nothing special about them aside from the fact that there's a greyscale step wedge included which is something anyone can do using ColorPort (that may have made a difference back in the days of the Epson x600 series and other earlier model printers but not so much anymore, at least from what I've seen). Aside from that, the math used to determine the patches is pretty much identical in Monaco Profiler, and i1Profiler. I've tested the addition of a greyscale test wedge for use in i1Profiler and I came to the conclusion that 1) in most cases it makes little if any difference and 2) sometimes it makes things worse. What's sometimes a bit more advantageous is some patches just outside of a perfect grey and you'll notice that i1Profiler actually adds these in if you choose a number of patches that isn't a multiple of x^3, otherwise the Atkinson Profiles and the numbers i1Profiler generates are are pretty much identical. The Atkinson generated profiles are 16 bits and i1Profiler is generating 8 bit profiles but I don't see that this has any practical advantage because regardless of the amount of precision your reference has, you're still measuring with the same amount of precision and when compared to the reference it's going to be a certain amount off. It's all relative in that sense. Now, if i1Profiler is incapable of using 16 bit reference data then using the Atkinson profiles can actually introduce errors into your profiles. I asked whether or not i1Profiler could handle 16 bit reference data and I never got a straight answer.
Toss the Atkinson profiles aside, i1Profiler has a (theoretically... there's fine print) MUCH better method of generating charts and that's the optimization feature which measures the response of your printer, and then generates a custom set of patches based upon those measurements. Sounds pretty slick but as far as large format inkjet printers are concerned (I'm sure that there are other printing technologies where this does help), it makes no discernible difference in a print, at least when you're working with targets that start with 800 or more patches.
My recommendation is to just use the i1Profiler generated patches. If you want to get those patches that don't conform to the even distribution of colors then set the patch count to x^3 - 1 (so 728, 999, 1330, 1727 patches, etc.). I'd encourage you to experiment though. There's no magic formula for what's going to work best in all cases because everyone's needs/equipment/aesthetic values, etc are different.
Cheers, Joe