So which one is good to use from Service or Method to get data from Web service?
Since we don't know anything about the data why don't you try doing it both ways, compare the results, and share your findings back here?
Use System#currentTimeMillis to obtain the start and end time for the call. Difference between these two values will tell you how much time a Service takes and how much time a Method takes
On a side note, did you know the service will use a method to fetch the data?
On another side note check out http://developer.android.com/reference/android/os/AsyncTask.html