I find useful the definition in Goold Brown's The Grammar of English Grammars:
A conjunction is a word used to connect words or sentences in construction, and to show the dependence of the terms so connected, as as, "Thou and he are happy, because you are good."
A preposition is a word used to express some relation of different things or thoughts to each other, and is generally placed before a noun or a pronoun.
[...] conjunctions, (except the introductory correspondents,) join words or sentences together, showing their relation either to each other or to something else; prepositions, though naturally subject themselves to something going before, assume the government of the terms which follow them, and in this they differ from all the rest.
[...][conjunctives] take the same case after as before them.
In he claims not to own anything other than his home, other than refers to, and governs, the noun home, and therefore is a preposition. In they observe rather than act, rather than connects two verbs that are equal in rights: observe and act, and therefore is a conjunction.
Notice that in the first example the nouns anything and home are not equal in rights, but the former is subordinated to the latter. This can be proven by observing
that, for the phrase to make sense, the first term must be more general than the second, and
that the second term is always in the objective case because of the government by other than, whereas the first may be in the nominative or the objective depending on the role of the whole phrase in the sentence: Any place (nominative) other than your home (objective) will be suitable for the party.