A particle moves from point $A(0,0)$ to point $B(1,3)$ along a complex spiral path $C_1$, while a second particle moves from $A$ to $B$ along a simple straight line segment $C_2$. If both particles are acted upon by a conservative force field $\mathbf{F}$, how does the work $W_1$ done on the first particle compare to the work $W_2$ done on the second particle?