Resize results are pretty well all subjective.
What looks good for one person, is not necessarily good for another person.
Basically their is no 'mathematical metric' that can tell you if some filter is better than another.
This is a chicken-egg problem. You can not compare results with a "perfect resize" because their is no such thing as a perfect resize! You can only do subjective (test group) comparisons.
Typically however the defaults are 'reasonable' and generally accept as being good by various experts.
You can try different filters (some sharper, some with ringing, some blocky or producing aliasing effects)
See Resize artifacts
You can try the photoshop method of doing a resize and then a small 'unsharp' image sharping operation.
See Sharpen Resized Images, whcih compares 'filter sharpen, against post resize unsharpen)
ASIDE: unsharp is a simpler (faster, though not by much) technique than true sharpen technique.
See 'Un-sharpen' Images using Blurs
Verses: Sharpening Images with Edge Detection
Also you can do from the typical 2-pass linear filtering to a 1-pass cylindrical (elliptical or EWA) filtering method that often produes better (less blocky and aliased) diagonals. but is also much slower.
See Distort Resize vs Resize