Tribological properties depend on the hardness, roughness, types of layers and the difference between them. In addition, this method is often influenced by the test method. It is known that with increasing hardness, wear resistance increases at the expense of reducing impact resistance. Friction is highly dependent on roughness. At high roughness and high hardness, brittle fractures are observed. At low roughness and high hardness the appearance of cracked distributed subforms of scales and chipping is established.
I agree with the answer of dr. Emil Hristov Yankov, I want to add an explanation. The real contact between surfaces depends on the condition of boundary lubrication, where high roughness in the surface leads to excessive wear and more takeover during the tribological corrosion. where increasing the surface hardness increase the abrasion wear occurs during initial wear as a result of the sliding, and after the initial wear as a result of the effects of the hard particles removed from the material. more details in the reference;
I agree with previous answers, and I would like to add some comments. Tribological properties depends also on other factors that could dominates your tribological system. The nature of the sliding parts, environment, dry or lubricated contacts, and the wear map should be considered carefully. Surely hardness is important when abrasive wear is dominant wear mechanism, but without neglecting other material properties such as microstructure, toughness, Young's modulus, etc.. All material's properties should be taken into account and be correlated with the dominant wear mechanism controlling wear and friction properties of your tribosystem.
It is known that the end result of the wear process is material removal. By definition, the hardness of a part is defined as its resistance to penetration. A high hardness means a high resistance and therefore a low penetration (of the penetrator). If we talk about the correlation between penetration and removal, it means that for a part that requires a high force to achieve the desired indentation depth, it also means that a high force is required to remove the grain from the reference position. Hence the higher the hardness the higher the resistance to material removal.