Here's the simplified view of a former naval architect (an engineer who designs ships) regarding ship motions (trying my best to avoid engineering jargon):
The motion of the ship is looked at as being a combination of three linear components (surge, heave, sway) and three rotational components (pitch, yaw, roll) (see definitions below). The center of motion for all six of these components is the center of gravity of the ship. Assuming that the ship is a rigid body and doesn't significantly flex (not precisely true but it's OK for this discussion) the three linear motions act equally at all locations on the ship. That is, the ship heaves (up and down) as though you held a piece of lumber in your hand and moved it vertically up and down ... the entire piece of lumber moves an equal amount vertically regardless of your location on the lumber.
However, the rotational motions, which are also centered at the ship's center of gravity, are characterized by increasing movement the further you are located from the center of that rotation. The further from the center of gravity, the more you feel that motion. Think of a carousel ... the further from the center the faster you are moving. Now if the carousel were designed to frequently reverse direction you can imagine how much more that would affect you the further from the center you were located. If you don't like that comparison, think of a see-saw ... near the pivot point you don't move very much; the further away from the center, the more you move up and down.
Now, the motion that you feel at any point on the ship is the combination of all six motions. Again, the three linear motions are felt equally throughout the ship. But, the three rotational motions (pitch, yaw, roll) are all felt more the farther that you are from the center of gravity. So, the lowest total motion is felt at the ship's center of gravity and the combined motion increases with increasing distance from the center of gravity.
Although the center of gravity can vary somewhat, for the purposes of this discussion you can assume with pretty good certainty that the center of gravity is located as follows:
fore/aft location = about midship
port/starboard location = on ship's centerline
vertical location = several feet BELOW the waterline
With this information, and the understanding that nearly all ship passenger staterooms are located above the ship's waterline, we can deduce that the lowest ship motions are felt on the lowest possible passenger stateroom deck, closest to midship and nearest to the ship's centerline. This would indicate the advantage of the inside cabin for lower motions.
However, the way that any individual responds to those motions can vary greatly between people, and as a previous poster noted, some feel better in an outside cabin because they can focus on the horizon and minimize the confusing messages that their eyes and ears independently send to their brain.
I hope that this helps somebody by providing the technical reasoning that leads to the "conventional wisdom" which was provided by a previous poster.
Some definitions:
Linear motion: Movement ALONG an axis
Surge: A fore and aft motion along the longitudinal axis
Sway: A port and starboard motion along the athwartship axis
Heave: A vertical (up and down) motion along the vertical axis
Rotational motion: Movement AROUND an axis
Pitch: A rotational motion around the athwartship (port and starboard) axis
Roll: A rotational motion around the ships longitudinal (fore and aft) axis
Yaw: A rotational motion around the ships vertical axis