It depends.
To start with there's a bit of an Apples & Oranges situation here. The Analysis -> Mass Properties -> Area Using Curves will only work with 2D profiles while the Analysis -> Measure Face will work with a free-form surface. Now what that means is that the second method is more general than the first which usually means that it's more of an approximation method while the 2D profile of curves can be a bit more precise.
Now if your profile of curves consist of ONLY lines and arcs, you should be getting the exact answer as long as the curves lie on the X-Y plane of the WCS. However, if the profile contains any splines, then there will be some approximation, but even then you have the option of changing the tolerance used for the calculations so in those cases you can tighten it up if you wish an even more accurate result (note that changing the tolerance only has an effect if the profile contains curves other then only lines and arcs).
Now as for the Measure Face routine, this does NOT provide any options for the user to control the tolerance, but the system will use a very precise value, it's just that by definition, it will still be an approximation.
So the rule of thumb should be for the most accurate answer:
If it's a 2D profile of only lines and arcs, use Analysis -> Mass Properties -> Area Using Curves.
If it's a 2D profile of curves that includes splines, still use Analysis -> Mass Properties -> Area Using Curves but if you feel it's critical, change the tolerance to few decimal places.
Of course if it's a 3D free-form sheet body you don't really have any choice.
Now before some goes and suggests this, IF you were given a 2D bounded plane ONLY (ie, not the original boundary curves that it was created from). I would NOT extract the a set of edge curves and then use Analysis -> Mass Properties -> Area Using Curves, but rather just use the Analysis -> Measure Face since extracting the edge curves could introduce additional approximations into the 'equation' and I would expect it to be best to work with as close to the original geometry as possible.
John R. Baker, P.E.
Product 'Evangelist'
NX Design
Siemens PLM Software Inc.
Cypress, CA
