There usually isn’t one universally “best” resampling algorithm. The right choice depends on the image content and the look you want.

General rule: choose based on what details matter most:

• Sharp edges, lines, text, pixel art, or simple graphics: methods like nearest neighbor can preserve hard edges better, but may create jagged artifacts.
• Smooth tones, gradients, and natural photos: interpolation methods often look better because they smooth transitions, but they can also soften real detail and edges.

So the trade-off is typically:

• edge preservation vs.
• smoothness / anti-aliasing
• with possible side effects like blurring or edge halos.

For many images, especially photographs, personal preference matters a lot—different viewers may prefer different results from the same file. In practice, the best approach is to identify the important features in the image, try a few methods, and compare the results at the final display size.

Good educational references mentioned by the community include Cambridge in Colour’s tutorials on interpolation, web resizing, and enlargement, plus comparison charts showing how algorithms differ in blur, aliasing, and halos.