Circuit 1 contains an inductor of inductance \(L_0\) and a resistor of resistance \(R_0\), while Circuit 2 contains an inductor of inductance \(2L_0\) and a resistor of resistance \(2R_0\). Both circuits are connected to identical ideal batteries of electromotive force \(\mathcal{E}_0\) for a time \(t \gg \tau\), where \(\tau = \dfrac{L_0}{R_0}\) is their common inductive time constant. At time \(t = 0\), the battery in each circuit is instantaneously removed and replaced with an ideal conducting wire, allowing each inductor to discharge through its connected resistor. Which circuit initially stores a greater magnetic energy just before \(t = 0\), and which circuit experiences a greater peak rate of Joule heating in its resistor during the discharge?