Which type auto encoder gives best results for text
A working example of a Variational Autoencoder for Text Generation in Keras can be found here.

Cross-entropy loss, aka log loss, measures the performance of a model whose output is a probability value between 0 and 1 for classification. Cross-entropy loss goes up as the predicted probability diverges from the actual label. In the case of character-by-character autoencoder, each character in the vocabulary would be a label.

Cross-entropy works if the input and output are the same size, that is the case in character-by-character autoencoder. Often times in text analysis, the input and output sequences are different lengths so a second term, encoder loss, is added to the objective function.