How to find out if two datasets are close to each other?
You could take an Information Theory approach by finding the lowest Kullback–Leibler divergence between the distributions. There is a KL divergence option within SciPy's entropy function.

&gt;&gt;&gt; from scipy.stats import entropy

&gt;&gt;&gt; p = [0.21,0.24,0.36,0.56,0.67,0.72,0.74,0.83,0.84,0.87] # Data removed to make equal sizes: [0.91,0.94,0.97]
&gt;&gt;&gt; q_1 = [0.13,0.21,0.27,0.34,0.36,0.45,0.49,0.65,0.66,0.90]
&gt;&gt;&gt; print(entropy(p, q_1)) 
0.019822015024454846

&gt;&gt;&gt; q_2 =[0.14,0.18,0.19,0.33,0.45,0.47,0.55,0.75,0.78,0.82]
&gt;&gt;&gt; print(entropy(p, q_2))
0.01737229446663193


The second simulated distribution is closer than the first simulated distribution to the real distribution.

If you are interested in inference, you could run many simulations and compute p-values. That process is a variation of permutation testing.