2400 x 600 should produce a smoother gradient from Left to Right or Right to Left, due to having 2400 dots horizontally instead of only 1200. More dots translates into more apparent gray scale levels.
Likewise, the 1200 x 1200 dpi should produce a smoother gradient from top to bottom based on having 1200 vertical dots per inch to work with versus 600.
Print resolution is always expressed in dots-per-inch (dpi). That is the number of dots produced on the paper per inch. Resolution indicates the quality of the printed output. A higher number of dots generally result in better quality.