I'm going to correct your terminology here.....
An "RTA" is a "real time analyzer" - which means that you watch a meter or display and it shows you, in real time, what's going on.
"FFT" is a "fast fourier transform" and is a way of calculating the level over a given range of frequencies.
(So an RTA can use FFT or not, and a device that uses FFTs can be an RTA or not... and most modern computer-based RTAs use FFTs.)
The main difference between the various measurement methods is the time scale....
Let's assume you have a speaker, sitting in the middle of an empty field, with a microphone positioned ten feet in front of it.
You measure the frequency response (it doesn't matter which method in this situation) and find that your speaker is flat.
Now, let's put that same speaker into a room - let's call it a solid cement walled bunker.
And, now, lets measure it specifically with a meter - manually - sat ten feet in front of the speaker.
We'll play a test tone, read the meter, write down the number, then repeat that with twenty or thirty different tones.
And let's assume that, in this particular case, we also get a result that looks pretty flat.
(Note that our meter readings
ALWAYS take a few seconds to set up and read.)
Now, just for fun, let's hang some heavy rugs on all the walls in our bunker.
Now, we'll measure it again with our meter....
Wanna guess what results you'll get?
You'll find that you now have a major roll-off in the treble.... maybe down 10 dB at 10 kHz.
Gee, but I thought we were measuring the same sound, coming from the same speaker, with the same meter.... so what happened?
Well, with a meter and a test tone, in "open air" - you are pretty much measuring the sound from the speaker.
But, when you move into a room, you're actually measuring the sum of the sound coming from the speaker, and all the sound bouncing around the room.
When we added the carpet, we made it so that high frequencies get absorbed more quickly than the low frequencies, so they don't bounce around as long.
If you do a little vague math, you'll see that this means that, after a few seconds, most of the high frequencies that would have been bouncing around got "eaten up" by the carpets on the walls.
But the low frequencies bounce around longer, and so get more chance to "build up" over several seconds... because carpets don't absorb low frequencies nearly as well as high frequencies.
Welcome to "Room Acoustics 101".
When you take measurements with a meter, or with an RTA and a continuous noise source, you're measuring the "long term average frequency response".
Sometimes referred to as "the power response".
This measurement is affected by the acoustics of the room - so you're
NOT getting an accurate measure of the speaker itself.
However, you
ARE getting an accurate measure of the room and speaker when taken as a system.
So, how would you take an accurate measurement of
JUST THE SPEAKER, but do it in a room.
Well, basically, you would take your measurement
QUICKLY.
If your room is ten feet square, and you put your microphone five feet in front of the speaker, and then turn your test tone on and take a measurement in 5 milliseconds,
you'll get to measure the sound coming directly from the speaker (five feet takes five milliseconds), but
BEFORE any of the reflections from the room make it back to the microphone.
(This is called windowing - and "lets you isolate the direct measurements".)
Another trickier way to do this is to play a chirp tone, then look very carefully at only one frequency at a time.....
and you pick things so you're looking at the
PART of it that's going straight from the speaker to the microphone, and ignoring the later reflections at that frequency
(because, by the time those later reflections arrive you've moved on, and you're looking at a different frequency).
This is the reason for those chirp tones.
A steady test tone (like pink noise) and an RTA takes a long-term average reading.
A slow sweep is in between - but pretty well a long term reading.
And a fast chirp tone is probably designed to let you measure what's coming from the speaker - and minimize the effects of the room.
OK, but which is "best" ("most accurate")?
Well, that's a more complicated problem.
The shortest/fastest reading is going to tell you the most about
JUST THE SPEAKER (great for designing speakers).
The slowest one is going to tell you the most about the long term performance of the entire speaker/room system (good for bass room correction).
And both are correct.
But... it's even more complicated that that... because music is sort of in between...
Some notes have time to build for a while, while others happen very quickly, so the echoes arrive separately (and never get time to add to the original level).
Now you know why we have all those
OTHER graphs.....
If you plot a T60 graph, it will tell you how long sounds take to die down (how live the room is)
AT EACH FREQUENCY.
(So, for example, our cement walled bunker might have a T60 that is relatively a straight line.
But, when we add the rugs on the walls, the T60 stays the same at low frequencies, but now it gets shorter at higher frequencies.
This is a scientific way of saying that our bunker is dead at high frequencies - and exactly how much.
This result will tell us
HOW we should expect the measurements we took with the first method to differ from each other.
My point, however, is that a chirp tone and an RTA reading may be very different.... but both may also be accurate.
They're different because they're telling you different things.
Now, to take our example.....
Let's assume that we started off with speakers that were pretty flat.
Then we put them in our fully carpet-lined bunker.
And we found that music sounds dull and dead in that room.
What should we do?
Well, we could trust our RTA measurement, and boost the treble by 10 dB on our EQ.
That will give us a relatively flat long term or power response.
But, because we've boosted the output of the speakers themselves, music might sound a bit shrill and harsh.
Instruments that play for a few seconds will sound just right, but drum hits and sharp sibilants may be exaggerated.
(In order to make the average response flat, we've made the short term response 10 dB too bright...)
Or, we could trust our chirp-tone windowed measurement, and believe that the speakers are flat.
And, by looking at both of those measurements, and noticing that the power response is way down at high frequencies,
conclude that the room has too much absorption going on at high frequencies.
And, once we figure that out, we'll take down a few of those rugs - which will probably make the room sound right.
(And we won't have sacrificed a worse result one way for a better one the other.)
Now, obviously, this wasn't as simple as it looked to begin with.
And we haven't even mentioned
WHICH rugs we should keep and which ones we should remove yet
And we didn't even go into how the dispersion of the speakers at different frequencies comes into all this...
(Most pros wouldn't bother to run a T60 graph... they'd just clap their hands, or shout "check", and listen to the way the echoes sound.)
Personally, assuming that I've already made sure the room is "reasonable", and I don't want to be there all day,
I'd probably adjust the room for "more or less flat" with white noise and a 1/3 octave RTA... and go from there with more adjustments only if necessary.
(You'll find plenty of books on what to do next... although you'll also find that the authors don't necessarily
AGREE on the best choices.
For example, most people agree that one half of the room should be live, and the other half should be dead.....
but the argument about whether the front or the back should be the dead half has been going on for about a hundred years
. )
My real point here is that picking out one particular graph, and trying to make that one perfect, rarely produces an optimum solution.
An RTA with pink noise can be useful to speed up the process of finding the best speaker placement and listening position by quickly weeding out speaker/listener locations that are causing *gross* peaks and nulls; RTA is no way near accurate enough to perform detailed analysis.
You're right, but 1/3 octave RTA helps get your speakers placed and tweaked before playing with EQ, and it can help doing basic EQ settings. FFT gives very detailed information, but is more difficult to work with.
sweet 
. )
