There are two factors at work here, and both relate to the tyre profile.
The first is similar to what motorcyclists know as ‘white lining’. A motorcycle squirms as it crosses a white line painted on the road.
What happens is that the tyre has a contact patch which is quite wide. On a motorcycle the contact patch can be 2 or 3 inches wide.
In the centre of the tread, the wheel has a given diameter. At the edge of the tread, the diameter is slightly less. If there is a wide contact patch, then the tyre contacts the road with one part of the tyre which is maximum diameter, and one part which is a smaller diameter - and all the diameters in between.
If the tyre is running across a slope - e.g. on a cambered road surface, then the maximum diameter is at one side of the contact patch (more or less) and the minimum diameter is at the other side of the contact patch.
This means that for every revolution of the tyre, the centre of the tread tries to travel a certain distance along the road, and the edge of the tread tries to travel a shorter distance along the road. The same tyre is trying to cover two different distances per revolution (and all the intermediate distances). This causes the tyre to try to turn towards the part of the contact patch which has the smallest diameter. This is a similar effect to having a cone shaped tyre! So the tyre squirms as it tries to crawl up the camber of the road.
The other effect happens with tyres with a central ridge. These ridges exist to reduce the rolling resistance when the tyre is rolling straight ahead. In normal circumstances, the weight is distributed evenly on the part of the central ridge which is touching the road.
When you ride across a slope, the weight is not distributed evenly - the effect is to ‘smear’ the central ridge slightly as the weight of the uni pushes down the slope across the line of the central ridge. This distorts the central ridge and affects the handling of the tyre.
So, to answer the question: it’s the tyre which matters. In fact, with a bigger wheel, the first effect (‘white lining’) will be reduced because (say) a half inch difference in diameter across the contact patch is a smaller percentage difference on a large wheel.
Narrow tyres without central ridges have to be best for cambered roads.