Buckling load is primarily dependent on pressure, temperature and x-sectional area of steel, not necessarily on diameter, although that does usually mean more steel, it doesn't have to all the time. Rougher terrain will also tend to increase the buckly frequency, due to the installation deviation from a straight line, but that drops out if the seabed is smoothed. Buckle resistance is primarily a function of friction between pipe and soil, if pipe is placed on the mud surface. If pipe is in a trench, or rock dump is placed on top, you may be able to count on friction/cohesion of soil to resist axial load and the weight of any soil or rock, etc. placed on top to provide an anti-buckling stabilization force.
It would be hard to draw general conclusions based on diameter; larger lines have more steel area (axial load), but higher radius of gyration to resist buckling and they also tend to grow axially rather than buckle, since gain in load with diameter is not resisted by the same ratio of a gain in soil friction. Smaller pipelines would not develop so much axial load, since x-sectional area is usually smaller, so can become fixed by soil friction, stopping axial growth, increasing compression load and setting up a buckling response. Water depth doesn't have much to do with the buckling problem. I think a function of operating temperature and pressure might go the farthest. Next correlate to diameter.
From "BigInch's Extremely simple theory of everything."