Yes, the current is definitely the same :)
The power dissipation doesn't have to be equal - it's bigger for a bigger resistance. But I'm pretty sure you do not feel the power dissipation as heat, it is negligible. The effect is probably due to high voltage that tickles the nerves. So it should be proportional. It's therefore not conceptually correct to consider the power dissipated, but may lead to the right results. Though I think the maximal E-field is more important than the net voltage.
Try touching anothers arm with your finger, and also vice versa. This makes a big difference, I always noticed, the finger feels much less. This may of course be due to less sensitive skin on the fingertips (which is even more the case if you play the guitar or something like this).
But it is also because the more curved surface will have a lower potential to produce the same field in air, which is what counts for the discharge. So maybe the "lightning" is broader near the more curved surface, since the treshhold for ionization is easier reached there, whereas it concentrates on one point near the flat surface.
Edit: In the experiment with the key described in the comment you see, that a big cross section through which the current can flow makes you feel less.
I have not completely understood this, it is an interesting question. One should probably also make a test, if the direction of the current makes a difference...