Confused by report discrepancies

1. The location command's XYZ are coming from the active alignment whereas the Geometric Tolerance position values are coming from the ABC datum reference frame.
2. The features and datums are calculated differently - DEFAULT math for the geometric tolerance command (constrained L2) as opposed to whatever math you had selected when measuring the features for the location command (least squares, min-sep, max inscribed, min circumscribed, fixed rad).
3. The geometric tolerance position is reporting the end point (it always reports the worst end of the cylinder - whichever that may be) whereas the location command reports the ACTL values from the feature.  If it's an auto cylinder, this will be the end you clicked when creating it, if it's a constructed or measured cylinder, the ACTL values will be the centroid.

I can see where your 3rd bullet would contribute to the differences. This brings up another question -  If I use legacy dimensioning, pc dimis will report the actual measured results as seen in the location command. Is one method better / more accurate /  more "correct"? My instinct tells me it depends on the application for the feature in question.

It depends on how closely you want to follow the standards.  Legacy dimensions are based on the active alignment, which is based on the way you measured the features.  There is no intelligence / validity checking, the onus is on the user to interpret the drawing and do everything correctly - it will let you do pretty much anything you want (be that right or wrong).  The Geometric Tolerance command takes care of that for you, you simply build the feature control frame, select the feature(s) you want to report and it interprets it.  It has inbuilt intelligence that checks the validity of the inputs against the rules of whichever standard you are working to (ASME Y14.5 or ISO1101).  If something is wrong, you will get a warning or error message.  It is also not affected by the feature fitting calculations that may have been employed when measuring features.  Instead, it takes the raw hits from the features and (when set to DEFAULT) applies datum math, feature math and tolerance math calculations according to the rules of the standard you have selected.  

Traditional CMM feature fitting math and the way alignments work result in limitations when it comes to trying to simulate datum reference frames for GD&T.  Most CMM software default to simple, least squares calculations for feature measurement because they are quick (don't need much processing power), widely understood and provide stable, repeatable results.  Many software packages have other feature math options such as Minimum Separation (Chebyshev) Maximum Inscribed, Minimum Circumscribed, but, whilst they do satisfy some of the requirements or the standards, they are generally less mathematically stable and less repeatable than least squares.

The standards have specific requirements such as constrained L2 (ASME Y14.5) or constrained min/max (ISO1101) for solving datum features.  The standards also have rules of datum precedence (which degrees of freedom features can constrain and the order in which those constraints are applied).  ASME Y14.5 requires datum features to be constrained both in orientation and location to each other whereas ISO1101 only requires datum features be constrained in orientation to each other - this is impossible to achieve with traditional CMM alignments.

As you say, the way you approach a measurement depends on the application but in general, if you are trying to verify a GD&T specification, the Geometric Tolerance command will be a better choice than legacy dimensioning.

I don't have much experience (almost 2 years), but in class we were taught that you should use Geometric Tolerance if you have a CAD model, and if you don't have it, you should use legacy dimensioning, is that true?

I practiced a lot with creating programs and, correct me if I'm wrong, I drew conclusions from all my exercises and from this forum, of course, by reading and practicing a lot, that more than half of the success is alignment, and if you create the correct alignment, it doesn't matter what you use Geometric Tolerance or legacy dimensioning, there is a minimal difference between them.

Malgorzata said:

I don't have much experience (almost 2 years), but in class we were taught that you should use Geometric Tolerance if you have a CAD model, and if you don't have it, you should use legacy dimensioning, is that true?

Generally yes.  It's not that you can't use geometric tolerance commands without a CAD model, it's just that it's much easier if you have CAD.  Without a CAD model you would have to manually edit all of your THEO X,Y,Z,I,J,K and Diameter values to ensure they were correct to the drawing.

Malgorzata said:

I practiced a lot with creating programs and, correct me if I'm wrong, I drew conclusions from all my exercises and from this forum, of course, by reading and practicing a lot, that more than half of the success is alignment,

Again, generally, getting the alignment right is a fundamental part of C|M|M programming so yes, aligning the part correctly will minimise errors.  

Malgorzata said:

if you create the correct alignment, it doesn't matter what you use Geometric Tolerance or legacy dimensioning, there is a minimal difference between them.

With this point, I have to disagree.  As I pointed out, the different fitting math and the fact that the geometric tolerance command can create orientation & location constrained datum reference frames make it superior to legacy dimensioning.

I know that there is a different mathematics used for Geometric Tolerance, but I haven't come across a big difference between them yet. There's still everything ahead of me... Thank you for the clarification! 

I know that there is a different mathematics used for Geometric Tolerance, but I haven't come across a big difference between them yet. There's still everything ahead of me... Thank you for the clarification! 

The only thing that comes immediately to mind would be projection error for cylinders. The "location" of the top of the cylinder could be well within tolerance, however the bottom of the cylinder could be way off location due to a drill wandering. So, your resulting angled hole would measure good with legacy, and good with a solid alignment, but bad with GD&T because the Demon "KNOWS" the hole is all wonky and really isn't in tolerance.