Pipeline in Bagging or Bagging in Pipeline

Hi,

Would we obtain different predictions for the two following models ?
In that case, what would be the difference?

model_1 = make_pipeline(
preprocessor,
BaggingClassifier(estimator=DecisionTreeClassifier())
)

model_2 = BaggingClassifier(estimator=make_pipeline(
preprocessor,
DecisionTreeClassifier()
))

In the first case the preprocessing is applied first and then bagging is applied on the preprocessed data.

In the second case, you apply preprocessing to each bootstrapped dataset.

It seems like the first makes more sense mostly because it is simpler. In practice, I would not expect too much difference between the two.

Thank you for your answer.