For objects exactly on ecliptic lines "planet od horizon" vs. "planet on Asc" (also 'planet on Midheaven' and 'planet in culmination') are the same. The farther away the planet is from ecliptic, the bigger the difference is. Practically, for ancient planets ( Sun through Saturn) this difference is too small to bother yourself with it, except places very near poles (north of Norway). For some of the modern planets (Ceres, Pluto, Kora - UB313, especially the latter two) these lines can be as much as few countries away from each other even nor far away from equator. Which one you use and which one will work for you you must decide for yourself. From my limited experience with them I neglect planet on horizon and planet on culmination and go with line "planet conjunction Asc" and "planet conjunction MC". This is opposite to what I do with planet's house position, where I neglect ecliptic projection of the planet and go with it's position in space relative to house cusps in space.