FEC is like EC is for ambient exposure...it tells the flash meter that the subject is brighter/darker than the meter usually expects, so it needs to give more/less output than it would without FEC. Metering is Automatic and makes life less complex for the photographer, although some of the control is given up in the process.
Manual flash power gives total control to the photographer, but with that control comes the burden of always keeping track of how far your subject is, and as subject distance (from flash) changes, it is necessry to adjust aperture selection on the camera. Moving from 8' to 11' from subject, you have to open up +1EV on the aperture, for example. Zoom heads make that even more difficult because not only does the Guide Number change with power (1/1. 1/2. 1/4, etc.) but it also changes with FL coverage (50mm has GN130 at 1/1, GN65 at 1/4; 105mm has GN190 for FF coverage at 1/1, GN95 at 1/4)