The issue isn’t forwards, it is down.
You have a tungsten rod held in a clamp on a satellite in a nominally stable orbit. Releasing the clamp just means the tungsten rod is now in essentially the same nominally stable orbit as the satellite.
To deorbit it, you need to meaningfully change its velocity. As tungsten is very dense, that takes a lot of fuel. The more fuel that is used, the sooner the rod will hit the ground and the higher the angle.
Simply dropping it means you have to wait months or years for the orbit to naturally decay, a lot of energy will be lost to atmospheric friction, and there is little control over the impact point. Not exactly what you want in your WMD.
The momentum is the same, the impulse (and therefore forces) are very different. The bullet is propelled down the barrel gradually - the force is spread through the entire time it takes the bullet to travel the length of the barrel, the reaction forces are applied to the stock gradually, and spread over the area of contact between the shooter and the gun.
A bullet stopped by a vest/plate has a much larger impulse. The bullet needs to be stopped essentially immediately, rather than gradually slowed down over a length equivalent to a rifle barrel, otherwise it kills you. The force is also more concentrated, occuring over the cross-sectional area of the bullet, rather than over the entire contact surface with the rifle.