Whole Sign vs Placidus Houses
Neither system is more accurate in the sense the question usually means, because the two do not measure the same thing. Whole sign houses take the sign as the house: the sign rising is the first house in its entirety, the next sign the second, and so on, twelve houses of thirty degrees each. Placidus divides the space above and below the horizon by time, trisecting the arc each degree of the ecliptic travels from the horizon to the meridian, and gives houses of unequal size with cusps at particular degrees. Hellenistic and much of medieval astrology, and Jyotisha throughout, use whole signs; Placidus has been the default of modern Western astrology since the nineteenth century and of most software. A practising astrologer chooses by purpose, and many use both at once.
Whole sign houses
In the whole sign system the Ascendant is a degree within the first house, not its starting point. An Ascendant at 25 degrees of Leo makes all of Leo the first house, from 0 to 30 degrees, and Virgo the second. A planet at 2 degrees of Leo, rising twenty-three degrees before the Ascendant and, by quadrant reckoning, in the twelfth house, is in the first. Each house has one sign and therefore one ruler; the topics of a house are read through that ruler with no ambiguity about intercepted signs or cusps that fall in the middle of a sign.
This is the system of Vettius Valens, of Dorotheus, and of the Hellenistic astrologers generally, and the one the Hellenistic revival, Chris Brennan and Demetra George among its authors, has restored to English-language practice. It is also the rashi chakra of Jyotisha, in which the lagna's sign is the first bhava and no other division is needed for most delineation. Its techniques of timing depend on it: annual profections count signs, not degrees, and the lord of the year is the lord of the whole sign profected to.
Placidus houses
Placidus, named for Placidus de Titis, the seventeenth-century Italian who systematised it, divides the diurnal semi-arc of each ecliptic degree, the time it spends between rising and culminating, into three equal parts, and the nocturnal semi-arc likewise. Its cusps are the Ascendant, the Midheaven, the Descendant, the Imum Coeli, and eight intermediate cusps derived from those arcs. Houses grow lopsided at high latitudes, and the system fails altogether inside the polar circles, where some degrees never rise. Its wide use follows from the tables of houses printed in the nineteenth-century English ephemerides, Raphael's above all, and then from the defaults of computer programs.
Placidus gives, as any quadrant system does, an exact treatment of angularity. A planet at 28 degrees of Leo with the Ascendant at 25 degrees of Leo is three degrees below the horizon and in the first house; a planet at 2 degrees of Leo is in the twelfth and, in the traditional judgement, weak and hidden. This is what quadrant houses are for: the strength and visibility of a planet by its distance from the angles. Ptolemy allows the five degrees above the Ascendant to count with the first house, and Lilly applies the same rule to every cusp; the rule shows that the older quadrant practice, like the whole sign practice, treated the horizon and meridian as points of power and not only as boundaries of topics.
How the decision is made
The tradition's own practice separates two questions. Which house holds a topic is answered by whole signs: the seventh sign from the Ascendant rules marriage, its lord is the lord of marriage, and a planet anywhere in that sign concerns marriage. How strong a planet is, and whether it is angular, succedent, or cadent in the sense that produces events, is answered by its degree relative to the horizon and the meridian, and a quadrant system gives that. The Midheaven degree is then read wherever it falls in the whole sign chart. It commonly falls in the tenth sign but may fall in the ninth or the eleventh, and when it does the tradition holds that the sign holding it takes on tenth-house significance in addition to its own.
Modern psychological astrology grew up on Placidus, and its delineations of intercepted signs and unequal houses assume it; a reading in that tradition uses it. Horary in Lilly's manner uses Regiomontanus, not Placidus, and Morin used Regiomontanus for nativities; the choice among quadrant systems is a second question, and Placidus has no claim over the others beyond its currency. Vedic practice adds the bhava chalit, a cusp-based chart on the Sripati or equal method, to the rashi chart, and reads a planet close to a cusp into the neighbouring bhava; the whole sign chart still governs the lords and the yogas.
A chart calculated in both systems shows quickly where they disagree: a planet within a few degrees of a cusp, an Ascendant in the last degrees of its sign, a birth far from the equator. Where they agree, which is most of the time for a birth at moderate latitude with a mid-sign Ascendant, the question does not arise, and the reading is the same in either.