Final RF envelope of FM and AM are the same
Let me start by saying that the document you refer to compares AM with narrow-band FM and I would expect pretty similar results. Narrow-band FM is not used by music broadcast stations just in case you were wondering and my previous mentions of FM in other questions were based around conventional broadcast type FM.

Why is it narrow band - 



Conventional broadcast modulators have a frequency deviation of 75kHz and generally limit the audio baseband to 15kHz. In other words the ratio of deviation to baseband width for broadcast is 5:1 whereas the document you are referring to has a ratio of 0.25 - that's a whopping difference of 20:1 and so you need to compare apples with apples.

I also note that in the linked document there is a discrepency in the amplitudes of the AM and FM signals. See below: -



Now this doesn't seem reasonable but it may be explained by someone!! With a mind to examining the total power in the AM and n-b FM cases, it seems to me that the AM signal with its double sidebands has much more power than the FM signal. 

Hopefully someone might explain this discrepency in my thought process. I guess I'm looking at how much blue ink there are on both diagrams and there appears to be more blue (and hence power delivered to an antenna) in the AM case compared to the FM case.

In short I have doubts about this document with respect to what it is trying to demonstrate and its methods.

And now, to the OP's question (at long last)


  Effective RF electromagnetic power profile is effectively the same for
  baseband audio content modulated by AM or FM. Question, Is this right?


According to the linked document it is not. However, there is no doubt that it should be and for narrow band FM versus AM I would expect about the same resiliance to broadband noise. I would also point out that resiliance to broadband noise is of academic interest but is not, by any means the whole story in determining system A against system B.