Similarity Measure of Simulated Time Series vs Observed time Series
in my opinion you can do the following to compare your simulated with your actual data.

Use usual measurements like  those you would use in predictions vs actual data:


RMSE
MAE (Mean Absolut Error)
MSE (Mean Squared Error) --> Gives greater weight to larger errors/gaps


Another statistical test that comes to my mind to test "prediction" quality between different models is the Diebold-Mariano test. It is fully implemented in R. As far as I know, not in any Python Library so far.

As a statistical test you could have a look at the distribution (but as you dealing with time-series you may face "memory", meaning that observations t and t+1 face autocorrelation (against most of statistical tests, as they assume independent observations). Autocorrelation seems to be the case for your data series. Therefore you should have a look on the % change of your sample data (from t to t1) and look if both series are drawn from the same distirbution - You can perform the kolmogorov smirnov test.

Hope this helps.

EDIT 

Regarding your question concerning smoothing and interpolation. Empiricis (not statistics) is more a trial and error concept. It really depends on your data behavior.