How do the views and outlooks and accomplishments of Greece and Rome compare to those of Western Europe during the Middle Ages and Renaissance?
This question seems to be addressing the intellectual and cultural achievements of the classical world versus those of medieval and Renaissance Europe. So this answer will not include a discussion of the military, diplomatic, or, for the most part, political achievements of either. The simplest way to answer such a broad question is to say that the cultural achievements and indeed the outlook of the medieval period and Renaissance era were heavily influenced by the Greeks and the Romans. While we usually associate the medieval period as a sort of intellectual backwater, it actually featured a great deal of creative thought. While the outlook was decidedly religious in nature, tending to regard mankind as debased in comparison with the divine, it nevertheless drew on a classical worldview advanced by Aristotle. The medieval philosophy known as Scholasticism, often associated with Thomas Aquinas, for example, was strongly influenced by Aristotle.
The most explicit evocation of Greek and Roman thought, however, came with the Renaissance. Humanism, the philosophy that guided Renaissance thinkers, writers, and artists, emphasized a return to what were believed to be the classical ideals of the ancient Greeks and Romans. Scorning what they thought to be medieval ignorance, they turned especially to Roman writers like Livy and Ovid to celebrate man, his achievements, and his potential. They viewed Greek and Roman philosophers and writers as possessing knowledge that had been lost during the Middle Ages. In terms of outlook, we must speak very generally, but it is safe to say that the worldview of the Italian Renaissance in particular had more in common with the secularism of some Greek and Roman philosophers (Epicurus, for example) than that of the medieval period. The critical worldview embraced by the Greeks in particular resonated with Renaissance philosophers, and the example of participatory government based on a virtuous citizenry set by Romans of the Republican period was emulated by Machiavelli, among others.