The orbital example where BDF loses momentum is really about the difference between a second-order method (BDF2) and a fourth-order method (RK), rather than explicit vs implicit (but: no method with order > 2 can be A-stable; since the whole point of implict methods is to achieve stability, the higher order BDF formulas are relatively niche).

There are whole families of _symplectic_ integrators that conserve physical quantities and are much more suitable for this sort of problem than either option discussed. Even a low-order symplectic method will conserve momentum on an example like this.