Does anybody know a statistical test to check if two samples are coming from distributions with the same means but different variances (Gaussian or more general)?
I immediately thought of the Kolmogorov-Smirnov test, which tests equality for two distributions by comparing their cumulative distribution functions. This would certainly tell apart those two distributions, but is not specific for a change in variance (you could reject the null hypothesis because of a difference in higher moments).
I think you may be looking for Bartlett's test of equivariance, which assumes normality (Gaussian distributions) and tests for equal variances. According to the link above, Levene's test is less sensitive to non-normality. These are all two sample tests, I think the chi-squared test can also be used to tell whether the variance is different from a specified value of variance.
Does anyone have experience in any of these tests?
The Bartlett test is used to test for equality of variances. I would use the Bartlett statistic, and look at it in two ways:
(1) compute percentage points from the chi-square distribution (that follows from assuming that the underlying distributions are Gaussian), and
(2) empirically construct a distribution of the statistic by randomly permuting the class labels (bootstrap).
If the results of (1) and (2) are roughly the same, then one can use either. If the results are different, then I would look more carefully at the data to see what went wrong (the distributions may be very non-Gaussian, eg bimodal), and take the results of (2) as the more conservative answer.
Ansari-Bradley two-sample test for equal dispersions.
This is a test of the hypothesis that two independent samples, come from the same distribution, against the alternative that they come from distributions that have the same median and shape but different dispersions (e.g. variances).
MATLAB has a function for it.
[h,p] = ansaribradley(X,Y)