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.
There is no fundamental reason why AM cannot support the same dynamic range as FM. You can vary the amplitude of a carrier over as wide a range as you can deviate its frequency. The fundamental limitation on dynamic range of any information carrying medium is noise. In this respect, FM can be superior to AM but the tradeoff is bandwidth. An FM signal will have a better signal-to-noise ratio than AM (hence the better performance of commercial FM broadcasts than AM) but at the cost of greater bandwidth. Sending a 1 kHz signal with AM requires a bandwidth of about 2 kHz. Using commercial FM requires about 150 kHz. You can't get something for nothing.
Best Answer
Neither, there is no modulation involved. The magnetization on the media is directly (and hopefully fairly linearly) related to the waveform amplitude.
There is a high frequency bias signal added to the audio signal, to get the resulting signal on the tape to a linear range of the magnetization curve, but the signal at the head is a sum of the two, not a modulation.
That image is from here, a good description of the process. This is stressing my memory of tape decks I had 40 years ago... The one instance I recall of amplitude modulation (kinda) was Dolby HX, which changed to amplitude of the bias in response to high amplitude audio signals, to keep the resulting signal from going into saturation. https://en.wikipedia.org/wiki/Dolby_noise-reduction_system#Dolby_HX/HX-Pro