Goodness of fit for two samples with uneven different sizes I have 2 different samples and would like to test a hypothesis about some aspect of their distribution. The first sample has 11,000 observations but the second is just 150 outcomes.
From graphically comparison, isn't clear if they come from the same population or not.
I tried to perform some Statistical hypothesis testing, but the main problem that I met is the large size of the first sample respect the second. I don't think that a method of Monte Carlo, to improve the size of the second sample, would be a good idea (except for graphically comparison maybe), because at that point I will have 2 large samples and any little different from them would be statistically significant.
So, is it a good way trying to resample from the first sample in order to get a smaller one? And at this point perform a hypothesis test.
 A: The effect of having a small second sample is reduced power. This may be an issue depending on the hypothesis. The issue is not the imbalance, but rather the sample size in the smaller group. 150 is not that bad.
In simulation studies you can see, the power of the T-test with unbalanced sample sizes lies between the power when both samples have the smaller sample size (conservative case) and the one sample test where the larger population estimate is taken as fixed (anticonservative case). If you are using the T-test, 150 is considered a decently large sample, and so reduced power is not an issue.
On the other hand, there may be heterogeneity in error terms due to unmeasured confounders, precision variables, or sources of correlation: cases that are typically handled by regression models. Regression models require more power to perform more adjustments for these heterogeneity-causing traits. If you find 150 does not give adequate power, consider matching instead. Select participants among the 11,000 who align closely 1-1 with the participants in the 150 to obtain a matched sample of 300 people who are balanced. 
If you find you cannot match the sample as fine as you would like, you can in fact conclude that they do not come from the same population and inference is not possible.
