J_J,
I would suggest that your are "lumping" behavior. In a strictly mathematical sense, yes, variations in settling time should be observed as variations in the frequency domain. However such is a "gross" measurement. What if in fact the differences are on the order of 0.5 to 0.1 dB? And what if the spectra of these variations is rather narrow (say no more than 10 to 100 Hz). Will our "coarse" measurements of swept frequency response actually catch these deviations?
If you did it right, yes. Of course, it's even easier to do this with an allpass sequence and deconvolution. Still, yes, it should and it will. There is no "gross" or "fine" here, if one shows the result, then the other should as well. If it doesn't, the measurement is bad.
Consider what a long tail means on a minimum-phase signal. It means, specifically, that the bandwidth of the system is narrower. The relationship df * dt >= c where df is the frequency resolution and dt is the time resolution is, as they say, not just a law, it's the math
(n.b. there the 'c' may change depending on the standard of resolution you use, but is typically expressed either as .5 or 1 for pure Gaussians at sigma, and is worse for other shapes of signal or frequency response)
So, unless there is non-minimum-phase behavior (like the fellow after commented on compensation warned about) a longer impulse response is a narrower system bandwidth, and the two had better show exactly the same results. If not, you either have a bad measurement or a nonlinear system, and if you show nonlinearity in a wire at line level or speaker level, something is wrong.
The key of catching variations, using the simplest deconvolution techniques (see
www.aes.org/sections/pnw/ppt.htm for the FFT class, recordings, and freeware) is to have a signal at least twice as long in time as you want resolution in Hz. It's not hard to do this, and signals of length 32k or 64k are not that hard to create. (see Johnston/Smirnov AES paper or Fezjo/Johnston/Bartlett/etc AES paper for various ways to do it) So, I most often use a signal that gives me .25 Hz resolution, give or take a bit.
You seem like you can probably digest the entire FFT tutorial, I'd recommend it, because you can also grab your own impulse response measurements if you want, there.
Remember to make cable measurements in-situ, so you see the effects of source and load impedence!