Which resolution to use? Max or closet match?

Hi all,

I just got a new bridge camera for work, and while i'm fairly handy with photography in general, one thing does escape me - optimal resolution to shoot at for the specific use of the image.

Say i need to send someone a 1920x1080 image (to show on their 1080p screen;
do i A: take the picture with the maximum resolution possible (4608x3456 @ 4:3)
or B: take it with the resolution that fits closest to the users screen (2048x1536 @ 4:3)

Which do i choose? Which would look best on their screen?

Is the image quality negatively affected by the image being downscaled to the monitors resolution?

Cheers for any and all advice lads,

CC.