How to decide which method to use TFIDF, or BOW
There is no specific way to deal with these kinds of experimentation. Below are some important points to remember before doing experimentation

If you are using NN to do the work, dense vectors like word2vec or fasttext may give better results than BoW/TfIdf

If you have more OOV words then fasttext may give better output than basic Word2Vec

If you are using linear algorithms like Logistic Regression/Linear SVM, BoW/TfIdf may have some advantage over averaging all the word vectors in the sentence. But it's not always true.

For the tree-based algorithms, training time may increase if we use BoW/TfIdf features because of the huge feature-length.