Logistic regression vs. cox proportional hazards model-which model to choose?

#1
I want to understand which model to choose for my task and advantage/disadvantage of each model. Basically, I am working on longitudinal patients data. I want to build a model to understand the factors associated with patient rehospitalisation within two years from the day they have been discharged. Some of the factors are age, location, chronic disease, number of GP visits etc.

One of the published paper which we are referencing is using cox proportional model to report hazard ratio. I don't know the model and its theory behind it. I am planning to use logistic regression and use the odd ratio to report the relative contribution of each independent variable to the dependent variable. Majority of my independent variables are categorical variables.

Could any statistician explain why I should use cox proportional hazards model instead of Logistic regression? If I choose logistic regression over cox model, what is the disadvantage of it? Will the strength of odd ratio report similar relative contribution of each independent variable to the dependent variable as hazard ratio? Greatly appreciate your help - Thank you
 
#3
Cox would address unequal follow-up times and loss-to-follow issues. In addition, you would be able to examine the outcome across the follow-up time. If all rehospitalizations occurred within 14 days and you just looked at rehospitalization any time within 2-yrs - yes/no; you would not know this. But the biggest reason is you state you have "longitudinal data", so use the model that addresses time.