okay i woke up to find that this has generated a ridiculous amount of discussion so let me lay out my thinking here. Let me start with a few assumptions:
A portal is a single 2D object with two sides, not two objects. it is effectively just a hole in the universe that connects two points in space, like a wormhole, and there is 0 distance between the two sides.
Portals are free energy devices, by virtue of the fact that if you place one above another you get to take infinite advantage of gravity and accelerate to terminal velocity (or infinitely, if there's no air resistance). Basically, they allow you to arbirarily increase the amount of energy - or potential energy - an object has purely by virtue of it's position. If you walk through a portal at low elevation and exit it at high elevation, you have gained gravitational potential energy.
With this understanding in mind, the answer can only be B.
As many arguers in favor of A have suggested, let's imagine a doorway passing around you. You are floating in space and a doorway approaches you at a speed of ten m/s. It passes around you and then proceeds away from you at the same constant speed. your position has not changed, but you have experienced a doorway pass around you like that.
now imagine you are falling through space at a constant speed of ten m/s. below you is a doorway, and you fall through it. Lacking any other reference frame, the experience is identical to that of the doorway moving around you. You approach the doorway at 10m/s, you exit the doorway at 10/mps.
Now decouple the two sides of the doorway. One side is moving towards you at 10m/s. The other side it stationary, sitting right next to you. As the moving side of the doorway passes around you, you will exit the stationary doorway at the same relative speed, because relative to you and to the portal, there is no difference between falling into one side at 10m/s and the portal passing around you at 10m/s. The relative velocity between you and the moving side is constant, therefore the relative velocity between you and the stationary side must also be constant, and you will exit the stationary side going 10m/s.
If a train traveling at 10m/s with one half of a portal mounted on the front were to "hit" you, portal first, you would exit the other side traveling at that same 10m/s relative to the exit portal, regardless of the material conditions around the exit portal, like the rest of the world being stationary to it.
