Very interesting comparison... I'd say that the basic relationships between the two pairs of cultures are the same but that the details differ.
The major similarity is that in each case the one civilization is seen as the main cultural influence on the other. The Toltecs are seen as the forerunners of Aztec civilization, the Greeks are seen as a major influence on Roman civilization (especially in the more "cultural" aspects of Roman life like theater and poetry and in religion).
The difference here is that the Greeks were actually around when the Romans started coming to power. The Romans had Greek slaves and such who actually brought Greek culture to Rome. By contrast, the Toltecs and the Aztecs were not contemporaries. The Toltecs served more as a legendary set of predecessors who could legitimize the Aztecs' rule.