Hi Steven - that's an interesting question. I guess the brief answer is that they all measure different things in different ways.
Lord of the Geniture: in Planetdance, this algorithm is derived from the work of William Lilly. It is a way of determining which planet has the most essential and accidental dignity in the horoscope. Essential dignity is derived from a planet's placement in it's sign and is determined by rulership, exaltation, triplicity, bound/term and face. A planet's dignity, or lack of it, is determined by its detriment or fall. Accidental dignity is determined by the planet's placement by house and other factors such as relationship to the Sun, aspect and motion (speed, direction). Each factor is assigned a score, and the total of these scores is summed: the planet with the highest score, in theory, is the most powerful planet in the horoscope.
Victor of the Chart: the module in Planetdance is derived from the work of Ibn Ezra, the medieval Arabic astrologer. This is a different algorithm, that looks at the essential and accidental dignity of planets in relation to the five hylegical points: Sun, Moon, Ascendant, Fortune and Pre-Natal Lunation. In essence, the victor of the chart is the planet which holds most influence over these five soli-lunar factors in the horoscope. This may not be the same planet as the lord of the geniture. Accidental dignity is assigned on the basis of house position, and day and hour rulership.
Oikodespotes: this is taken from Hellenistic astrology. The oikodespotes is the ruler of the predominator of the chart. The predominator is the sect light and is identified by whether the chart is diurnal or nocturnal. The sun is the sect light of a diurnal chart if it is in a non-cadent house. The moon is the sect light of a nocturnal chart if it is in a non-cadent house. If both are in cadent houses, the ascendant becomes the predominator.
Atmakaraka: from Vedic astrology. In Jaimini, this point is the planet placed closest to the end of it's sign.
Case study: Donald Trump
All calculations use Egyptian bounds, sect-based day ruler and sect-based triplicity ruler
Victor of the Chart: Saturn
Lord of the Geniture: Mars (Saturn scores a lowly 5 - it's in detriment and peregrine - has no essential dignity, but has quite a lot of accidental dignity)
Oikodespotes: Mercury (ruler of the Sun, which is ruler of the ascendant)
It's important to consider the victor and lord of the geniture together. Saturn has a great deal of influence over the hylegical positions (Sun, Moon, Fortune, Ascendant and pre-natal lunation). We might say that the integration of these soli-lunar factors requires Saturnian discipline in Trump's case. However, Saturn is poorly dignified essentially (it's pretty much as difficult as it can be from this point of view), but has quite a lot of accidental dignity by house, solar relationship, speed and direction. Overall, we might conclude that Trump needs Saturnian discipline to master his soli-lunar factors, but he has little intrinsic Saturnian qualities himself. The accidental dignity of Saturn suggests that the discipline needed for this comes from the circumstances of his life rather than his character.
Mars has the most accidental and essential dignity in the chart, and is likely to (literally) lord it over the rest of his planets. However, Mars has little to do with the soli-lunar placements identified by the victor of the chart. Being highly angular in a fiery sign, gives him a very direct, intractable character (along with other factors such as temperament).
The oikodespotes is Mercury, ruler of the solar lord of the ascendant. This planet probably says a lot about Trump's approach to communication (it's in Cancer, in water) and how he uses it to reinforce his personal style (Sun in Gemini).
I hope that helps.
Ed
21 12' 06" 
15 40' 38" 
07 15' 55" 
06 18' 10" 
05 56' 46" 
r
15 35' 41" 
r
13 20' 13" 
24 13' 24" 
27 08' 15" 
00 30' 45" 
02 31' 00" 
r
19 08' 14" 
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