The intensity of the strong interaction, also known as the strong force or the strong nuclear force, does depend on the quarks involved. The strong force is the fundamental interaction that binds quarks together to form particles such as protons and neutrons.
The strength of the strong force between quarks is characterized by a property called "color charge." Quarks carry a color charge, which comes in three types: red, green, and blue. Antiquarks carry anticolor charge (antired, antigreen, and antiblue). The strong force acts between quarks by exchanging particles called gluons, which themselves carry color charge.
According to the theory of quantum chromodynamics (QCD), which describes the strong force, the interaction strength between two quarks depends on their color charges and the exchange of gluons. The rules governing the combination of quark colors and the behavior of gluons are quite complex, but they determine the overall strength of the strong interaction.
In the specific case you mentioned, comparing u-u and u-d quark combinations, the strong interaction strength can be different. For example, a proton consists of two up quarks (u) and one down quark (d), and the overall strong interaction between these quarks is determined by their color charges and the exchange of gluons. The interaction strength can vary depending on the specific combination of quarks involved.
In summary, the intensity of the strong interaction does depend on the quarks involved, their color charges, and the exchange of gluons between them. The detailed calculations of these interactions are complex and are described by the theory of quantum chromodynamics.