Which is likely to have more of an impact on supply and therefore market equilibrium: the demand for orange juice or the demand for a particular brand of orange juice?

Demand for orange juice would have more of an impact on supply and therefore market equilibrium.

This is because for a particular brand of juice, not much of the consumers would be affected as orange juice offered by different brands are treated as close substitutes. So, even if juice from one brand becomes scarce, consumers would have an option to switch to another brand for the (nearly) same juice.

However, for the orange juice market as a whole, any change in supply would force the consumer to change his/her preferences from orange juice to any another fruit juice, which will have more impact on market equilibrium.