Technology

In a car with ABS, two sets of tyres with different grip will have a different point at which tyres lock up, with grippier tires locking up later and ABS letting the brakes bite harder before acting.

Now a harder question is whether a tyre with less rolling resistance will be less grippy. All things equal, yes, it will. Tyres grip by deforming and creating friction in the contact patch, and the point of these tyres is to reduce friction.

To make up for this, manufacturers use clever designs (e.g. where tyres can deform more under certain conditions) so that they can retain characteristics similar to tyres with more rolling resistance. Of course, everything in engineering is a compromise, which means that A) these tyres are more expensive because of the additional complexity and B) the design and materials science can only go so far and they have indeed slightly less grip; otherwise all the tyres would be like this.

As an anecdote, Toyota sold the GR86 with Michelin Energy Saver tyres fitted as standard (in Europe at least) for "grip" reasons: they allowed the car to drift at really low speeds (some car journalists commented that it was remarkably easy to take roundabouts sideways at legal speeds).