@stevemz I would guess that the likely cause of the differences in NP and TSS has to do with what each of the applications does with certain data.
As you know, Andrew Coggan’s algorithm for calculating NP is the 4th root of the rolling 30sec averages raised to the 4th power (simplified wording: see p.120 of Training and Racing . . . ). So when the applications run the algorithm, there are several pieces of data for which the software needs to make decisions that may be handled differently by the different apps (presuming they all implement the formula correctly), including start of file, end of file, pauses, and spikes. As TSS is derived from NP, then if NP is high, TSS will be as well (you can see this in your Element data).
The only app that is “certain” to be accurate is TrainingPeaks (and, of course, WKO4) as it was “certified” by Dr. Coggan to correctly implement his algorithm. So errors in TP results would come from bad data.
A more controlled way to compare the units would be to create a new .fit file (from an effort) that has no pauses or backpedaling; import it into WK04, identify the start and end of your effort (where the first and last recorded wattages are located), delete all data points in the .fit file prior to and after those points, and reimport the updated .fit file into the apps and see if the NP and TSS results are the same. [note: I have used this approach successfully to remove power spikes where I know, for example, I didn’t generate 2x pMax).
As for 30sec max and KJ there seem to be no standards, such as with NP and TSS, such that one app could be presumed to be better than the other.
As you can infer above, WK04, for me is the gold standard for all power-based data and use it (and TP Premium) for all cycling (and multi-sport) data analytics. For users new to power-based metrics or don’t have the time for a deep-dive understanding of what TP/WK04 provides, I think TR has done a great job at simplifying all of it and providing a subset that they feel is necessary to help users become faster cyclists. So even if the analytics aren’t perfectly accurate, it is likely that it is “close enough” and consistent from effort to effort.