There were a number of differences between Greek and Roman mythology and religion. Something that is important to remember is that they both sprung from the same source of Proto-Indo-European religion and mythology, some of which we have reconstructed. While they did influence one another, much of the similarity is from being divergent traditions, rather than convergent. Roman gods were not simply copies, but in fact the decedents of a more ancient mythology practiced by a common ancestor. That said, especially with regards to heroic and epic cycles there was a significant influence.

One of the major differences between Greek and Roman mythology is that the Greeks, through direct and prolonged formative contact with a number of Near-Eastern societies, absorbed a number of features of their religions, especially cosmological and numerological. The Ancient Greeks were lay at an important trade crossroads and had a significant contract in their early years with the Neo-Assyrian and Egyptian empires, both of which influenced Greek Mythology and religion. On top of this, the post-Mycenaean Greeks absorbed the beliefs and practices of the Mycenaean Greeks who also had sustained contact with the Near East that was perhaps equal to the later Greeks. Thus, Greece has a messier set of gods and a more chaotic cosmology than Rome. Or at least that is one hypothesis.

Near Eastern influence on Greek myth and religion is a somewhat controversial subject not the least because "Near East" is a nebulous term (does it mean Egyptian? Mesopotamian? Semitic? Anatolian? All?) and this leads to confusion. Second, we aren't sure how much works like Hesoid and Homer reflect actual ancient beliefs. Literary interpretations of the gods and myths may not have actually been accepted beyond their value as works of literature, certainly, they fulfilled a different role than a Christian Bible even if they were sacred in their own way. That said, it is highly probably that, like later works, these drew upon established mythological tradition and they reached a wide audience which may have informed their religious beliefs, especially since there is no known "canon" for religious practice in Ancient Greece like there was for other societies.

Roman Mythology and Religion is often thought to represent a "purer" version of Proto-Indo-European religion, having absorbed less from other religions than Greek and being more similar to the other Indo-European mythological fragments we have left. Therefore, it's gods and mythology are more structured in the sense of the PIE peoples. However, that isn't the only cause, Roman society often frowned upon the excesses of Greek society and prided itself on order and stoicism, befitting it's republican society. When it did absorb Greek influences, it often set itself counter to Greece, as a more sensible counterpart to a barbaric Greece.

You mentioned Zeus and Jupiter, and yeah, Jupiter is more...dignified to the modern reader. However, we have to understand that our perception is colored through the lens of literature and it should be understood that to the Greeks, Zeus' mercurial nature was part of his status as King of the Gods and worship of him was not just based around his power, but to them his wisdom.

• McEvilley, T. (2002). The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophy. New York: Allworth Press.

• Koenen, L. (1994). Greece, the Near East, and Egypt: Cyclic Destruction in Hesiod and the Catalogue of Women. Transactions of the American Philological Association (1974-), 124, 1-34. doi:10.2307/284283

• Allan, W. (2004). Religious Syncretism: The New Gods of Greek Tragedy. Harvard Studies in Classical Philology, 102, 113-155. doi:10.2307/4150035

• Virgil. Fagles, Robert (tr.). (2006) The Aenied. Penguin Classics, London, England.

• Nogel, Scott. (2006). "Greek Religion and the Ancient Near East". Blackwell Companion to Greek Religion pg. 21-37