I would argue that the probability of catching a line
is more dependent on the specific design of the boat than its keel type. As a broad generality, it would be easy to argue that it is equally probable to catch a line
on a full keel boat as on a fin keel boat. Its about the geometry. On a full keel the propeller
is closer to the bottom of the keel and a line
being dragged will lay back along the side of the full keel with now where else to go, and therefore have a greater percentage of a chance of getting caught.
On a many fin keels, the leading edge angle is similar to that of a full keel, yet the line
is more likely to miss the prop since there is a longer distance between the root and the keel tip and there is a greater separation between the keel and the prop.
Now then, if you are talking about some of the newer vertical edge fins with bulbs on the bottom, or a fin keel with a sail drive, those designs probably are more prone to getting a line in their prop.
And yes I know that full keel types still believe the old saw that full keels do not catch lines, or foul their props, or damage their rudders as easily, but that does not make those superstitions true.