What do you like best?
A comprehensive collection of advanced or special-use statistical and regression functions. Having access to models and statistical tests related to those models in the same package is very handy. Additionally, for regression models such as ARMA/ARIMA/ARIMAX/SARIMAX, the output already contains a lot of relevant information like AIC and BIC score.
What do you dislike?
Output type is inconsistent and can be a hurdle at times. For example some methods will output a list, others a dictionary, etc, which can make using a statsmodels output as an input somewhere else a little tricky. Documentation is also inconsistent.
Recommendations to others considering the product:
Just be aware that outputs from very similar functions aren't necessarily consistent with one another. Some processing is often necessary for use with more standard libraries numpy, pandas, etc.
What problems are you solving with the product? What benefits have you realized?
I primarily use statsmodels for time series analysis and regression modeling. Having tests such as augmented dickey-fuller and ACF/PACF functions built in are very useful when prepping data for an ARIMA model.