It isn't possible to say which of the two types of mutations would be more harmful to an organism as both forms affect the functioning of proteins in organisms in adverse ways and result in serious ailments.
Both missense as well as nonsense mutations result in an altered protein product which is unlikely to function as it should. The two differ only in the cause behind why this happens.
In a missense mutation, an entirely new amino acid is produced as the codon responsible for the protein is altered. Several diseases including Epidermolysis bullosa, sickle-cell disease, and SOD1 mediated ALS are the result of missense mutation.
On the other hand, in nonsense mutation one of the codons that specifies an amino acid is converted to a stop codon; this does not allow the protein to develop completely. The activity of the protein is dependent on where the stop codon is located and can be affected slightly or totally disabled. Several genetic illnesses result from this including DMD and thalassemia.