A robust (non-parametric) measure like Coefficient of Variation -- IQR/median, or alternative? For a given set of data, spread is often calculated either as the standard deviation or as the IQR (inter-quartile range).
Whereas a standard deviation is normalised (z-scores, etc.) and so can be used to compare the spread from two different populations, this is not the case with the IQR since the samples from two different populations could have values at two quite different scales,
 e.g. 
 Pop A:  100, 67, 89, 75, 120, ...
 Pop B:  19, 22, 43, 8, 12, ...

What I'm after is a robust (non-parametric) measure that I can use to compare the variation within different populations.
Choice 1:
IQR / Median -- this would be by analogy to the coefficient of variation, i.e. to $
\frac{\sigma}{\mu}$.
Choice 2:
Range / IQR
Question:  Which is the more meaningful measure for comparing variation between populations?  And if it is Choice 1, is Choice 2 useful for anything / meaningful, or is it a fundamentally flawed measure?
 A: "Choice 1" is what you want if you are using non-parametrics for the common purpose of reducing the effect of outliers.  Even if you're using it because of skew that also has the side effect of commonly having extreme values in the tail, that might be outliers.  Your "Choice 2" could be dramatically affected by outliers or any extreme values while the components of your first equation are relatively robust against them.  
[This will be a little dependent upon what kind of IQR you select (see the R help on quantile).]
A: I prefer not to compute measures like CV because I almost always have an arbitrary origin for the random variable.  Concerning the choice of a robust dispersion measure it is difficult to beat Gini's mean difference, which is the mean of all possible absolute values of differences between two observations.  For efficient computation see for example the R rms package GiniMd function.  Under normality, Gini's mean difference is 0.98 as efficient as the SD for estimating dispersion.
A: Like @John I have never heard of that definition of coefficient of variation. I wouldn't call it that if I used it, it will confuse people.
"Which is most useful?" will depend on what you want to use it for. Certainly choice 1 is more robust to outliers, if you are sure that is what you want.  But what is the purpose of comparing the two distributions? What are you trying to do? 
One alternative is to standardize both measures and then look at summaries.
Another is a QQ plot.
There are many others as well.
A: This paper presents two good robust alternatives for the coefficient of variation. One is the interquartile range divided by the median, that is:
IQR/median = (Q3-Q1)/median
The other is the median absolute deviation divided by the median, that is:
MAD/median
They compare them and conclude generaly speaking the second is a little less variable and probably better for most applications.
A: It's important to realize the minimum and maximum are often not very good statistics to use (i.e., they can fluctuate greatly from sample to sample, and don't follow a normal distribution as, say, the mean might due to the Central Limit Theorem).  As a result, the range is rarely a good choice for anything other than to state the range of this exact sample.  For a simple, nonparametric statistic to represent variability, the Inter-Quartile Range is much better.  However, while I see the analogy between IQR/median and the coefficient of variation, I don't think this is likely to be the best option.  
You may want to look into the median absolute deviation from the median (MADM).  That is:
$$
MADM = \text{median}(|x_i-\text{median}(\bf x)|)
$$
I suspect a better nonparametric analogy to the coefficient of variation would be MADM/median, rather than IQR/median.
A: The question implies that the standard deviation (SD) is somehow normalized so can be used to compare the variability of two different populations. Not so. As Peter and John said, this normalization is done as when calculating the coefficient of variation (CV), which equals SD/Mean. The SD is in in the same units as the original data. In contrast, the CV is a unitless ratio. 
Your choice 1 (IQR/Median) is analogous to the CV. Like the CV, it would only make sense when the data are ratio data. This means that zero is really zero. A weight of zero is no weight. A length of zero is no length. As a counter example, it would not make sense for temperature in C or F, as zero degrees temperature (C or F) does not mean there is no temperature. Simply switching between using C or F scale would give you a different value for the CV or for the ratio of IQR/Median, which makes both those ratios meaningless.
I agree with Peter and John that your second idea (Range/IQR) would not be very robust to outliers, so probably wouldn't be useful.
