I dont think this is possible in the general case. "No free lunch" and all that. I think you need to first form a null hypothesis, and then find evidence for/against the null hypothesis. And what you are trying to compare actually is probably not the data sets themselves, but the populations from which the datasets were sampled. I think it's safe to say that the datasets themselves are different? Since, if they were exactly identical, you wouldnt be asking the question :-)
But, for example, the distribution from which the first dataset was sampled might have some mean $\mu_1$, and the distribution from which the second dataset was sampled might have some mean $\mu_2$. Can you find evidence, using the sampled datasets, that the means are/arent the same?
So, an example null hypothesis could be $\mu_1 = \mu_2$, which you can then bring mathematical/statistical methods to be bear on to find evidence for or against.
In the general case, I dont reckon there is any definitive method to say that two datasets are/arent drawn from the same distribution. Since I think a valid distribution is to imagine a black box that gives the first dataset at time $t_1$, and the second dataset at time $t_2$. Or alternatively two black boxes, one that always gives the values of the first dataset, and the other that always gives the values in the second dataset, where the two black boxes thus represent two different underlying distributions. And there's no way to differentiate between these two cases, by looking at the two sampled datasets. (I think this is a bit hand-waving, and there's probably a formal way of expressing this, but I reckon the underlying concepts are probably approximately correct).
