Real time monitoring of Earth Orientation Parameters (EOP) requires gyroscopes with extreme rotation sensitivity. Although passive resonant gyroscopes (PRGs) theoretically offer a lower quantum noise limit than active ring laser gyroscopes (RLGs), their practical performance has historically lagged by over two orders of magnitude behind state-of-the-art RLGs (10-11 rad/s/√Hz). Here, we close this gap using the 64 m2 HUST-2 PRG. By systematically suppressing dominant technical noises, we achieve a rotation sensitivity of 3 × 10-11 rad/s/√Hz, reaching a performance comparable to the world's best RLGs. Furthermore, we establish a precise shot noise model and experimentally demonstrate a fundamental sensitivity limit of 5.7(1) × 10-13 rad/s/√Hz at 1 mW incident light power. These results confirm the system's potential for a further two orders of magnitude improvement, paving the way for high frequency EOP measurements and terrestrial tests of General Relativity.