In this link, a comparison is made between colors of cars, before reaching thermodynamic equillibrium.
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems.
If your two objects stay in the sunlight long enough to reach thermodynamic equillibrium, the zeroth law should say that their final temperatures are same:
The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third one, then they are in thermal equilibrium with each other.
See the explanation of thermal equilibrium here.
Figure 1.2.1: If thermometer A is in thermal equilibrium with object B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. Therefore, the reading on A stays the same when A is moved over to make contact with C.
Emissivity and absorptivity would play a role to how long it would take for the two different colored objects to reach thermodynamic equilibrium with the air surrounding them at the same input radiation.
The tests with cars show that the time is important in showing the differences in the color of the car, and the particular case has to be taken into account. I would think that the two pieces of different color paper ( no wind) should reach equilibrium in the noon sun fairly soon, and thus the same temperature. In general one should use the emissivity and absroptivity to solve a specific case, but it is not simple calculations.