Both scales were designed to estimate wind speed from damage produced. With time, as more data points were included, a trend line was produced that enables the prediction of possible damage given a wind speed. This is true with both scales. The advantage of using the EFS over the FS is that the EFS scale considers more variables (such as size of storm and duration) so the damage predictions are more accurate.
Consider this: the Saffir-Simpson Hurricane Wind Scale is used to predict damage based on hurricane maximum sustained winds. This is analogous to the Fujita Scale. However, it doesn't always do a good job of predicting damage because it fails to consider factors such as size of the storm and rate of forward motion. Typically a Cat 5 hurricane would be expected to do more damage than a Cat 3 hurricane, and a Cat 3 hurricane more damage than a Cat 1 hurricane. However, this isn't always the case. A small Cat 5 hurricane (Hurricane Camille) produced far less damage than an extremely large Cat 3 hurricane (Hurricane Katrina). A Cat 1 hurricane that stalled out in Mobile Bay for three days did more damage than would be expected from a Cat 3 hurricane moving at a typical 5-8 mph. If there was a hurricane scale that considered total area under hurricane winds, the duration of the hurricane winds, damage predictions for hurricanes would be much more precise - this hypothetical hurricane wind scale is analogous to the Enhanced Fujita Scale.
Hope this helps clarify.