Click on the diagram for a larger view.
In this diagram the trail in both cases is positive, because the contact patch lies behind the steering axis irrespective of its angle. The perpendicular distance between contact patch and steering axis is the effective trail. Ground trail and effective trail differ in that the latter is the actual length of the lever arm on which the side force acts when there is a slip angle. Slip angle occurs when the steering is turned and the contact patch is displaced away from the line of travel (as seen from above). This displacement causes a torque around the steering axis which tends to restore the steering to the straight-ahead position if the trail is positive. This effect is also referred to as the castor effect, which is the self-centering observed in castor wheels.
Other terms for steering axis angle are castor angle (or caster in American English) and rake angle. There is a close relation between steering axis angle and trail that is mediated by the fork offset which is the perpendicular distance between the wheel axle (or spindle) and the steering axis. For a given steering axis angle the trail depends on the offset. Positive offset is when the wheel spindle is situated in front of the steering axis. Negative offset is when the wheel spindle is situated behind the steering axis.
In the diagram we see a small positive offset is required to obtain the given trail with a 15 degree steering axis angle. The diagram clearly shows that with a suitable offset a headset with either postive or negative angle can have equal amounts of positive trail, but when the steering axis angle is negative the offset must be negative and quite large to obtain the same amount of positive trail.
Another exemplar is Frankenbike by Jeff Del Papa.
The following diagram illustrates two points which suggest that a negative angle is superior to a positive angle in terms of handling. Again it is a side-view using the same colour coding (red = positive, green = negative), but here the negative angle (15 degrees) has been exaggerated in order to show the difference more clearly. The diagram is a scale drawing of the lower part of a 20" wheel that has run up against a 2 cm obstruction in the road. The ground trail is 5 cm.
Click on the diagram for a larger view.
In the diagram the solid red and green lines perpendicular to the steering axis show the relative lengths of the lever arm. The difference here is exaggerated, because a 15 degrees negative angle is rarely seen in practice. More realistically, with a 7 degrees negative angle compared to a 15 degrees positive angle the difference in leverage is approximately 10%. Such a difference could represent a noticeable handling superiority in favour of negative steering axis angles.
In the case of positive steering axis angle the opposite applies: The steering head will fall whichever way the steering is turned, and we have an unstable equilibrium.
While these two equilibria clearly differ, their actual effect on handling may be very small or not apparent. However, the effect of a negative angle, if noticeable, would seem to be the more desireable of the two.
Any deflection of the wheel by an external force is countered by torque resulting from the slip angle, as already explained. Gyroscopic reactions can also deflect the wheel about the steering axis. Offset moves the center of gravity of the wheel away from the steering axis and thus increases the moment it has about the axis. The torque due to slip angle may be insufficient to counter these reactions and the result could be an uncontrolled wobble. Zero offset would minimize this likelihood and maximize the self-steering effect of positive trail.
As stated above, to obtain positive trail a negative angle demands a relatively large offset, while the same trail can be achieved with zero offset by a small positive steering axis angle. The difference may be very small if the mass of the wheel is small, but in the case of a front-wheel drive that mass can be quite large, and its interaction with other forces is compounded by the offset. This clearly is a disadvantage on the side of negative angles.