You should use GetxController when you want to use data on per open page. If you open the page GetxController will initialize and you will get update data.
But if you use GetxService, it will only get initialized once when the app launch first time. And the data would be saved in memory.
GetxService may hold the about local storage. You may need this data as soon as the app boots up or installed.
GetxService object will stay in the memory as long your app alive.
GetxController provides onInit() and onReady() method which are also good for data initialization. GetxController will die as soon as you leave a certain page or screen.