Why does MYIROtools offer its own profiling charts instead of simply using layouts like IT8/7.4 or similar?

Basically a chart which we use to finally create an ICC Profile shouldn't be named "profiling chart" but "characterization chart".
It's purpose is to get information about the behavior of an output process; in other words, to characterize the process.
That is the correlation between printed CMYK (or RGB or CMYKOGV etc.) value and resulting color.
Simplified, an ICC Profile is a file and/or data format to store this characteristic.
The most accurate characterization would have entries for all input values (16.7 million for an RGB device).
People who are familiar with ICC Profiling processes do know that no characterization chart has millions of patches.
Also the number of entries in an ICC Profile is limited to ensure efficiency in terms of storage space and processing speed.
Therefore it is absolutely possible to also limit the number of patches which are measured.

But how do we decide which patches we need to measure?

“Everything should be made as simple as possible, but no simpler.”

We like to have an accurate characterization of the output process using as few information as possible.

Technically this means that every printed color that we can predict by interpolation is unnecessary to measure.
A simple example is an oldschool CRT monitor. By knowing the color of white and 100% red it is very easy to predict the color of 50% red. The reason is the nearly perfect linearity of the cathod ray tube.
For a printing process this is typically true for primary ramps (e.g. 0%....100% Cyan) as a single ink is quite predictable.
On the other hand, the more ink we apply to a substrate the less predictable the result.
In addition certain printing processes or technologies have different behaviors in terms of predictability.

Conclusion:
To get an accurate characterization of an output process it is necessary to optimize the measurement points to reflect the non-linearities of this process. Charts which are described in ISO standards such as IT8/7.4 etc are good to check the accuracy of an output process. But they are not optimized to characterize a particular printing process. 

MYIROtools offers three different "standard" chart sizes. The smaller charts are subsets of the bigger charts. All are optimized to get information in areas of the gamut where typical printing processes behave unpredictable.

An additional criterion to consider when designing characterization charts is the algorithm of the profiling engine, especially for Multicolor charts. The MYIROtools charts are of course optimized for the MYIROtools engine.

How do I decide which chart I should use?

The question technically means: How many patches are enough to characterize my process?

You can test this yourself.

• Create a profile using the 420-patches chart (1)
• Print and measure the bigger chart
• Use MYIROtools Analyze and its feature "Easy Compare"
• Select the measurement of the small chart
• Load the ICC Profile from 1) as reference.

• Note the resulting color differences (6)
• Select the measurement of the bigger chart
• Load the ICC Profile from 1) as reference
• Check the resulting color differences and compare them against 6)

In case the color differences from step 9) are much bigger than the differences from 6) there is a good chance that your profile does not describe your printing process accurately enough. Make a profile with more patches and check again.
Please note that it could also be that your printer is unstable or prints non-uniform. This will cause a color difference between the prints from steps 1) and 2) already.