A coagulant-based disinfection will remove the microorganism via neutralizing their charge to make them form flocs. These flocs can either be removed via sand/gravel-based filtration or ultrafiltration and microfiltration. Depending upon the size of the microorganism, a required amount of setting time must be given to them to settle and get removed. As per gravitational law, the smaller the size, the higher time it will take to fall; therefore, for viruses and colloids, sometimes you might need a few months to years to get them settled (https://www.safewater.org/fact-sheets-1/2017/1/23/conventional-water-treatment). So, it will be helpful in removing bigger particles but not the smaller ones.
Chemical-based disinfectant basically interrupts the cellular metabolism of the microorganism by disrupting their metabolic enzymes. This process helps in killing the microorganism. In the case of a coagulant, it just removes the microorganism and does not kill (except for a few cases where the coagulants can also kill).
Coagulation is a well-known technique for the water treatment process as it helps in removing suspended particles, dissolved organic carbon and natural organic matter (NOM). Such substances can interfere with the chemical disinfection process and form side products. For example, in the case of chlorine-based disinfection, the presence of NOM can lead to the formation of tri-halomethanes which are carcinogenic in nature. Therefore, coagulation becomes important to remove these substances before disinfection as it makes the process easier.
As per your question, both techniques are useful depending upon the purpose of the use. Chemical-based disinfection is good as it can provide rapid disinfection and residual effect, which helps in preventing bacterial proliferation during water supply and storage. On the contrary, coagulant-based disinfection can remove the microorganism but will not be able to give a residual effect. Both techniques are useful on their own terms; however, combining them would make a more useful and safer disinfection process.