Research undertaken in the name of precision medicine may well open new vistas of science, and precision medicine itself may ultimately make critical contributions to a narrow set of conditions that are primarily genetically determind. For example, linking sub-populations, population data and grouping risk prone groups for chronic diseases or metabolic disorders could aid in disease prevention and development of novel treatment strategies. Talking in a layman way, there would be a huge benefit for public health by precision medicine as combination of approaches—ranging from population-wide interventions to specific interventions tailored to higher-risk groups—will be required to efficiently improve population health.

Personalized medicine has the purpose to provide an efficient therapy for each individual affected by a genetic disease. Recent advances in research revealed that most illnesses (not only cancers) are linked to genetic alterations or predisposition, making personalized therapy essential to heal nearly any disease.
The first advantage would be, as already mentioned by Rohit, an overall improvement of population's health. In second instance, it would provide huge benefits from an economical point of view. Currently, if a specific therapy is missing for a disease (or when conventional chemo/radiotherapy, which provides little benefits and many side effects, is the only option to cure a specific cancer), patients needs to be followed all-life-long, with significant costs for public health care. Personalized medicine would provide complete healing with no further need to expensive follow-up. In this meaning, personalized medicine works like a vaccine, which prevents people to get sick, allowing public health care system to save a lot of money that would be spent to cure them.

Adding a few recently published work into this discussion:

1. Friedman, Jan M., et al. "Genomic newborn screening: public health policy considerations and recommendations." BMC medical genomics 10.1 (2017): 9
2. https://bmcmedgenomics.biomedcentral.com/articles/10.1186/s12920-017-0247-4
3. King, Jaime S., and Monica E. Smith. "Whole-genome screening of newborns? the constitutional boundaries of state newborn screening programs." Pediatrics 137.Supplement 1 (2016): S8-S15.
4. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4939764/

I am a professor of pediatrics, so for sure I am biased toward the newborn poplulation.