If the physical size of the prints isn't changing, i.e. remaining 13.3 x 8.85 inches, then I would say stick to the larger image at 320 DPI. If you print the same size image at 160 versus 320 you'll have less printed dots per inch, meaning the physical resolution of the print is smaller, and I would argue the lines and curves in the image would appear less smooth at 160, and colour tones would graduate less smoothly too.

Have you thought about what might happen if you brought the resolution of the image down even further? let's say we halved it one more time, and then again, to 532 x 354. Would you print a 13.3 x 8.85 inch photograph at 40 DPI? Taking this further, you could arguably get down to only a few dots per inch. I'm confident the photo would look a lot less like a photo and just a splotch of colour.

Reducing the pixels on screen doesn't eliminate noise or other image artefacts - it just conceals them from your eyes. To achieve this effect in print, you need to pack more dots into an inch. The higher the number of pixels you have, the easier it is to pack more dots into every inch. If you have a 4256 x 2832 pixel image, and you printed at 320 DPI, you'd have a 13.3 x 8.85 inch photograph. If you printed that same image at 600 DPI, you'd have a 7.09 x 4.72 inch photograph. The latter would be smaller, but it would achieve the same visual effect as the on-screen pixel reduction.

Cheers