Mechanical action organs (AKA tracker organs) were built for many hundreds of years when the electricity hasn't been discovered yet. Even today historically conscious organ builders continue to build them. On such an instrument not only the bellows were operated by hand or by feet mostly by another person (sometimes even today) but also registration changes had to be made by hand, too.
The most obvious advantage of mechanical action organs is the ability to control an attack and release of notes. It another words, it's possible by gently feeling the pressure point just before the opening and closing of valves, to make these valves open or close faster or slower. This is really crucial in early music and in music of lyrical character. That's why it's best to keep the contact with the keys at all times and not to lift the fingers in the air whenever possible to control better the sound mechanical action organ creates.
The most obvious advantage of electro-pneumatic action organs is the ability of placing the console anywhere in the room. By the help of special cables organ consoles can be moved upon request very easily. This is very handy for organs in concert halls where organ is not used all the time or in situations where the organist has to be seen from any angle.
I have to point out of course that electro-pneumatic organ allows for sudden registration changes. You can program the stop combinations in advance and go from pianissimo to full organ and vice versa by one push of a button. Many Romantic and modern organ compositions require that kind of flexibility.
This flexibility is not unique for electro-pneumatic organs, though. Even mechanical action may have a system of ventils, foot pedals, or levers which help achieve sudden registration changes as well.
Try to be conscious of these aspects of both type of organs when you play them because one of the many of your requirements as an organist is to bring out the best that each instrument has to offer.
Writing in fingering and pedaling for Widor's Toccata. Editing Movement 2 of Sonate No. 1 for Organ (1968) by Teisutis Makačinas.Transposing hymn setting "Come, Ye Disconsolate". Practicing Exercise No. 1a and b, from 12 Technical Polyphonic and Rhythmic Studies Op. 125 by Oreste Ravanello (HT to Leon). Practicing Hanon "Virtuoso Pianist". Preparing for improvisation recital on August 8 "The Little Mermaid" at my church. Composing "Morning in the Countryside".