based on my previous knowledge, polymer based NPs are used for loading the therapeutic drugs, while metal NPs or metallic compound NPs are therapeutic agents, themselves as well as used as a carrier.
The main motive should be to have NPs with blunt edges. Sharp edged/highly crystalline NPs may damage the cell membranes of the healthy cells. For this, I feel, polymers are best suited.
I agree with Anubhav, as he pointed out correctly in the previous answer. Perhaps, the choice can not be generalized on the basis of their chemical nature. Organic and Inorganic are just two broad groups as a general classification scheme, however, this need not to reflect their functional abilities. In order to make a decision about the choice, a lot of factors like size, shape, chemical structure, reactivity and specificity have to be considered. Both polymers as well as inorganic nanoparticles have generated significant interest towards cancer therapy.
Following texts provide overview of both the approaches
PMID: 21104301 - Inorganic nanoparticles in cancer therapy
PMID: 19521593 - Polymer nanomaterials in organic chemistry