Traditional and modern methods of reading Scripture, it seems to me, are compatible. For a helpful introduction to the ancient Christian practice of lectio divina, try that of Luke Dysinger. For a defense of a religiously sensitive reading of the Bible in the historical-critical mode, try that of Marc Zvi Brettler.
On the other hand, I think that traditional methods of reading Scripture are often more respectful of Scripture than modern methods. Modern appropriation of Scripture, while necessary if one lives in modernity in a way a Yeshiva bocher or an Amish farmer does not, almost inevitably distorts the sense of the text to a greater degree than traditional rabbinic or traditional Christian appropriation. It need not be so, of course: the best modern historical exegesis defends the biblical text from ancient and modern mis-readers alike.
The historical approach to the study of the Bible in the best sense of the word is a magnificent intellectual adventure, an act of devotion in its own right.
It is doubtful, nonetheless, that a modern reader will ever match a rabbinic or patristic reader's utter familiarity with the details of the text. In the same way, the immersion of Luther and Calvin in the biblical text saved them from errors of ignorance frequent today. UPDATE: Kevin Edgecomb weighs in with a thoughtful post.