Which method to use to remove trend from time series?
Detrend does a least squares fit (linear or constant) and subtracts this from your data points. You can look this up in the docs.

Simply taking the difference between consecutive data points will in general lead to other results.

In general the regression based detrending seems to be more reasonable. You could also think about using random sample consensus (RANSAC) to be more robust to outliers.