Given the reflecting surface area of an orbital ring, it would seem to me that it would be like a permanent full moon on Earth's night time surface.
Jupiter has an albedo of 52 percent, while Earth's is 30. If you built a shell around it with atmosphere, land masses, oceans and enough focused sunlight to approximate Earth, it would be something like three times brighter and it's already a tremendously bright object.
If you built your Dyson Swarm inside Earth's orbit, how would you keep it from shading out Earth? If you built it outside, wouldn't it blot out most of the stars?