I like both, they are Masters; Verdi description of characters is very subtle and dramatic, he is also more prolific
For Verdi I like: La Traviatra, Aida, Don Carlo, La Forza Del Destino, Falstaff, Rigoletto, MacBeth, and most fav is Otello.
Puccini is very international: Turandot from China, The Girl from the Golden West (USA), Madame Butterfly from Japan, La Boheme from France, Tosca from Italy.