Much praise for the good old volumes of CAH and deservingly so, but can anyone recommend similar series with throrough approach that would give a fresher look on ancient (pre-Roman) history, providing more evidence in terms of monument inscriptions, quotations and findings?
It depends on what part of ancient history you're interested in. If you're looking for an overview of Ancient Greek history that shows you the primary material, I'd recommend Robin Osborne's Greece in the Making, 1200-479 BC (2nd ed. 2009), followed by Simon Hornblower's The Greek World, 479-323 BC (3rd ed. 2002). Unfortunately there isn't really a detailed textbook that covers both periods. If you're looking for a history of the Near East and Mesopotamia, the main textbook is Amélie Kuhrt's The Ancient Near East, c.3000-330 BC (1995).
Blackwell's Companion series has great volumes on just about every period of Ancient History (although the one on Persia isn't out yet); I'd particularly recommend the Companion to Archaic Greece (2009).