Yes, both scientists have different horizons. But this doesn't lead to information paradoxes, because their ability to communicate will also depend on their horizons.
Let's start with the cosmic particle horizon (the edge of the observable universe). Suppose that there is a distant galaxy near the edge of the current particle horizon of scientist 1, but still outside the particle horizon of scientist 2. For simplicity, suppose that both scientists and the galaxy lie on a straight line.
Now, scientist 1 observes the galaxy, which means that some of its photons have reached him. The exited scientist wants to send his observations to scientist 2. But during that time, some photons of the galaxies have passed scientist 1, and are on their way to scientist 2, ahead of the message. So by the time he gets the message from his colleague, he'll have observed the galaxy himself. That is, the galaxy has entered the particle horizon of scientist 2.
What about the cosmic event horizon? Suppose that a galaxy lies inside the current event horizon of scientist 1, but outside the current event horizon of scientist 2. If that galaxy sends out photons at the current cosmic time, they will reach scientist 1 at some point in the future, but they will never reach scientist 2. Will that lead to a paradox?
No, because when scientist 1 receives the photons, he himself will have moved outside the event horizon of scientist 2. So he'll never be able to communicate his observations to his colleague.