How to compare the qualities of two interpolation (image resizing) algorithms?
Usually to test interpolation algorithm (for resizing, but also rotation and all sorts of "reversible" image transforms, you would apply the forward algorithm several times (ie resize to twice the size, take the result and resize it to 1.5x the size, etc .) and then apply all the backward transformations. 

The more transforms you apply the more errors you will see and the more sensitive your comparison is. It can also represent your use case better (people pick an already resized image, resize it, and publish it)

Then you compute the max difference (or the standard deviation, or just visually compare) between the result and the original image.

In your case you can also apply all the forward transforms and then resize it once to the original size.