Why Kaplan-Meier approach is superior to using the Life table method for obtaining cumulative survival properties?
Quoting from the 7th edition of the AJCC Cancer Staging Manual (page 15):
The life table method was the first method generally used to describe cancer survival results... It is most useful when data are only available in grouped categories ... The Kaplan–Meier estimate utilizes individual survival times for each patient and is preferable when data are available in this form.
Thus, as Frank Harrell notes in a comment, if your life table has time broken down day-by-day it will provide the same results as a Kaplan-Meier model with a day-by-day time scale. If the life table has a coarser time breakdown into weeks, months or years, the corresponding survival curves will be less detailed than the Kaplan-Meier curve based on daily data, as drops in the survival curve from the life table can only occur each week, month, or year respectively.