This post applies to Sharepoint 2013 on Premise and Nintex Forms. I have not tested it on another versions, but I think it‘d happen the same.
Currently you can use a formula on the “Calculated Value” control available on Nintex Forms.
There is a particular behavior when you compare two columns of type person.
The case that works as expected 
I have 2 columns of type Person named PrimaryOwner and SecondaryOwner.
Both of them are equally configured.
Sharepoint List Configuration
Nintex Form Configuration
And then I use the control named “Calculated Value” that has a formula on a Nintex form comparing those 2 fields.
The result
Then I added an item on the Sharepoint List setting those 2 columns with the same user.
With those values the result of the calculated value is true.
So far, so good.
The case that doesn’t works as expected 
I have the same 2 columns of type Person named PrimaryOwner and SecondaryOwner.
Both of them are NOT equally configured. The difference is that I changed the property named “Show field” on the Sharepoint list settings for 1 of the columns.
The result
Without changing the saved values on the columns named “PrimaryOwner” and “SecondaryOwner” now the result of the calculated value is false.
I also tried using the runtime function named userEquals, but got the same results.
I do not know if it is considered a bug, but perhaps users expect that the comparison does not depend on the format of the field.
The current suggestion is to be careful when you use the Calculated Value control comparing columns of type Person.
I’ll try to talk with the support team so as to know their opinion.