It is a simple play on usage. The word 'wise' has as its first definition in the Cambridge English Dictionary as
B2 (approving) having or showing the ability to make good judgments, based on a deep understanding and experience of life:
The noun wisdom unequivocally refers a quality of sense and understanding. In CED:-
the ability to use your knowledge and experience to make good decisions and judgments
But the phrase being none the wiser or *being wise to something * relates to possessing information about something.
So the joke here involved what the French call a double-entendre. The judge is saying that he is no better informed than be was before the barrister started speaking. The barrister hits back by taking the word 'wiser' in the 'wisdom' sense of 'wiser'.
I would not recommend this type of insult in an actual court of law. The play on language is not an amusing witty 'dig': it is downright rude (a 'contempt', in effect). On the stage, however, the barrister safe and gets a laugh from the audience.