They are very different. Mother Saverini is simply seeking revenge for the death of her son. Her motivation is nothing other than her terrible grief at the loss of her dearly loved child. Moreover she is savage, and coldly calculating in her pursuit of the man who deprieved her son of life.
Hamlet is not simply exacting revenge and nor is he cold and calculating in the pursuit of his goal. Rather Hamlet is hesitant in his response to the news that his father was murdered and doubts the truth of the news he has heard from the ghost. Hamlet continues to be troubled and uncertain in the the face of growing realisation that he must act, but somehow cannot. Unlike mother Saverini Hamlet proves wild and imprecise in his destructive revenge, which leads to the death of not only his own mother, but a young and completely innocent lady - Ophelia.
Of course, it is Hamlet's doubt and confusion that make the play so memorable. Hamlet is not just a man seeking bloody revenge, but a young man trying to come to terms with the tragic circumstances of his life.