In examining the terms "traditional" and "modern," literary scholars will differ on the defining time periods or characteristics which qualify those classifications. The following are provided as a general guide:

• Characters in traditional literature are typically simple. They are presented without complex character arcs, and their struggle is therefore easily identified. Because of this, themes such as good vs evil are easy to determine, and it is clear which choice the character should make based on his rather simple personality. The main character is often a hero, saving others and demonstrating an innate moral goodness. Conversely, modern literature often presents characters with much more complexity. Their struggles are often so complicated that readers have a difficult time determining which choices the character should make. Readers are often unable to predict the conflict's resolution as characters find themselves embedded in complex situations. Main characters are rarely heroes who triumph over conflict but instead reflect people who resign themselves to surviving—and often barely do so.
• Plots in traditional literature are often simple; this was necessary, as they were often conveyed through an oral tradition to an often illiterate society. Simple plots allowed these stories to be told and retold through generations. Often in traditional literature, the plot's resolution pointed to a virtuous truth, such as the importance of inner beauty or the victory of good over evil. Modern literature, on the other hand, often involves complicated plots with various subplots. In a much more literate society, it is not necessary to keep the plot simple, and readers engage with various conflicts which happen simultaneously.
• Settings in traditional literature are often vague, allowing the stories to transcend time and place. They thus have a more universal appeal. In modern literature, settings are typically more rigidly defined, and often the setting is the source of conflict itself as a character struggles against the norms and expectations of his or her society.

The terms "traditional" and "modern" are vague ones, particularly when applied to literature as a whole rather than to particular genres of writing. These points, therefore, are generalizations, to which there will always be exceptions.

• Traditional literature tends to adhere closely to genre and form. A traditional poem, for instance, can be classified as epic, lyric, or elegy, or as a sonnet, a sestina, or a villanelle. Modern literature is harder to classify and often defies genre.
• Traditional literature is more likely to rely on archetypal characters and even on stereotypes. These characters' conduct is dictated by their social roles. Modern literature more often has characters acting against archetypes.
• Traditional literature invites readers to suspend their disbelief and immerse themselves in the story. Modern literature often draws attention to its own artificiality.
• Traditional literature is more likely to be didactic, with a religious message or a moral about how one ought to live. Modern literature often describes the way people act in a manner that is intended to be realistic, without making moral judgments about what they ought to have done.
• Following on from the last point, characters in traditional literature are more likely to get what they deserve. As Oscar Wilde put it, "The good ended happily, and the bad unhappily. That is what Fiction means." Even in tragedies, when the punishment seems unfair, there is a set of predictable rules. In modern literature, it is more common for immoral characters to escape punishment and for good people to suffer in the name of realism.

akannan's comments are good, so I'll start with some of those as my first bulleted point and add another point of my own:

• Traditional literature tends to be elitist (written by the very few for the very few). Modern literature tends to be a little more inclusive and more representative of the diversity of human experiences
• Traditional literature tends to follow set conventions (even when it sometimes parodies those conventions), such as the epic or sonnet or letter. Modern literature sometimes mixes up the conventions in very unexpected ways, striving not for harmony and unity but for dissonance and disunity.

You might want to review the introductions to the different chapters on the Perspectives on American Literature website (see the link below). It's fair, I think, to see the first two chapters, at least, largely as representative of traditional literature and the final two chapters largely as representative of modern literature.

In using the terms "traditional" and "modern," it's worth noting that the two are not mutually exclusively or tied simply to publication dates. In literature from centuries back we're always able to come across things that seem amazingly "modern," and most of our recently published literature is still much more "traditional" (at least in terms of structure and subject matter) than it is "modern."

This particular question will receive many point of offering, bullet-ed or not.  I think that you will also find many points of divergence in the answers offered.  One similarity between both visions of literature is that they both seek to articulate the human predicament.  Tolstoy once said that "All literature seeks to answer two fundamental questions:  Who are we and How shall we live?"  These two driving forces are present in modern and traditional literature.  Another critical point of comparison in both forms of literature is the investigation of human action and the complexity that lies within it.  Truly great literature from either time period offers an intricate view of human action and the many factors that initiate it.  I would say that one primary difference between modern literature with its traditional counterpart is that the former is more inclusive in terms of its representation.  Literature has been broadened to include different voices from different narratives and experiences in the modern setting.  At the same time, modern literature has more inter-textual forces which provide inspiration than traditional literature possessed.