In a nutshell, no-fault insurance relies on internal diplomacy and bargaining to resolve disputes and a tort system uses the power of the legal system. Imagine a no fault settlement as one that is decided in a comfortable office setting, and a tort settlement involving the full complement of legal advisors, a judge his assistants, and a jury to decide the verdict. It is easy to see how tort coverage could be more costly as well as more likely to bog down the claim for long periods, putting the injured people at risk of not getting sufficient treatment.
No fault insurance tends to be less expensive than traditional tort coverage. The concept of no fault insurance is that everyone is insured, and individual's claims are handled by that driver's insurance company. Insurance companies then negotiate settlements between themselves, without impeding the injured person's ability to get proper care.
On the potentially negative side, no fault insurance often means you are giving up your right to pursue legal avenues in regards to the claim. If a situation were to arise where you felt the at-fault driver owed you more than you were being awarded, having no fault coverage could leave you without any recourse.
There is no right or wrong choice. You have to weigh faster, less complicated claim settlements against the ability to file a suit if the claim does not go as you deserve and higher premiums. The tort system offers you more options for getting settlements, but if you never face a situation where you have to go beyond the default claims you can save a great deal by not having tort system coverage.