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I need a calculated field formula to compare two dates from two fields - and display the one that is the latest date.

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Try some of the following equations in the Calculated Column.

First option:

=TEXT(MAX(INT( FirstColumnName ),INT( SecondColumnName )), "dd-MM-yyyy hh:mm:ss")

The TEXT command allows you to format what is returned. In this case we're setting the integer value returned from MAX into a date/time format of [Day Number]-[Month number]-[Full year] [Hours]:[Minutes]:[Seconds]. Like noon today being 20-09-2018 12:00:00

Here's an example comparing the Created and Modified of a signup sheet:

Setup:

Setup

Result:

Result

Second Option:

If you're fine with the default formatting that SharePoint does you can also just check max and return a date/time value.

=MAX(INT( FirstColumnName ),INT( SecondColumnName ))

Here we got rid of the TEXT and just use the systems default formatting. Days are marked off as an integer and the hours/minutes are a fraction of some sort. So we let SharePoint decide how to display it by telling it the number returned from MAX is a date value.

Setup:

Setup 2

Result:

Result 2

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