If the length two boats is the same, and the lines are similar, but the beam is different, then the narrower boat should sink a bit lower in the water. That should reduce the center of gravity of the combination of boat and paddler. A lower center of gravity gives greater stability. So, although it may be counter-intuitive -- it is very possible for a narrower boat to be more stable than a wider one.

Four other points come up here. First, the lines have to be similar. If one boat is very pointy and the other is rather stout then comparing beam measurements may be fruitless. (That means you aren't even close enough to compare apples to oranges). 2) The narrower boat gets the added stability from a lower center of gravity, but that means the boat has greater draft. This may be fine for deep water, but you'll scrape the bottom in shallows more often.
3) the narrower beamed boat has less total displacement. If you swamp there will be less water to pump out, but for expeditions your ability to carry gear is reduced.

and then, 4) you have to consider the issue of rocker here.

If one of the boats has a straight keel, and the other has some rocker in it, then stability changes along with your turning radius. Consider a boat with enough rocker to raise the keel line at bow and stern, oh, about 3 inches above where the keel is at the middle of the boat. In comparison to a boat with a straight keel, the boat with some rocker will have greater draft at the middle of the boat when loaded with the same load. Consider how the water line changes as these boats are loaded.

assuming a 3 inch waterline on the straight keeled boat with a 150 pound load.
When both boats are floated empty, the rockered boat draws 1 1/2 inches of water, and the bow and stern are clearly out of the water. The straight boat draws 3/4 of an inch. With 75 pounds loaded in the rockered boat is drawing a hair over 3 inches at the center, and the bow and stern are finally in the water. the straight keeled boat is drawing 2 inches. With the final 75 pounds added, bringing the load to 150 pounds in each boat, the straight keeled boat comes to it's designed water line of three inches. that is the draft over the fulllenght of the keel. The rockered boat, though will sink a 1 1/2 inches more, giving a draft at bow and stern of just 1 1/2 inches, but the middle of the boat will be 4 1/2 inches deep. If that "load" is a paddler then they will be sitting 1 1/2 inches lower than a person in a straight keeled boat.

This is something like a hammock effect. The center of the boat is "swinging" a bit from the suspension at the bow and stern, which is higher than the middle. That is what gives you some additional stability. In order to turn over you would actually have to lift the bottom of the boat more (by about 1 1/2 inches) than with a straight keeled boat. I don;t want to draw too close to an analogy to a hammock here, as the boat is supported along its entire surface by the water it is floating in -- unlike a hammock which is only held at the ends -- but the effect is similar. Put your weight in the middle and the sag of a hammock is like the rocker of a rigid kayak, or the flexing of a S-O-F kayak. the paddler's weight and center of gravity drop and stability is increased.

hope this helps

PGJ