Most of the general assumptions people have about resizing may not be applicable to tilesets because pixel art is very different from a photograph or drawing to the interpolators used when resizing.
The thing is, I do have a bit of experience in pixel art. I consider myself something of an amateur artist. I've made various kinds of art both on the computer and on paper. And on occasion I have made some pixel art.
Yes, pixel art
is very different from a photograph or drawing, especially in terms of interpolation and resizing. But,
if anything, properly resizing pixel art is vastly more important to pixel art than it is for photographs or drawings. Due to the purpose and nature of pixel art, artists generally try to squeeze in as much detail as possible in a small area. Much of that is designed on a pixel by pixel basis, with it being common for single pixels or pixel-wide lines to represent important details. So loosing any of that detail to resizing is often
very noticeable.
(For example, squeezing a 20x20 pixel image down to, say, 16x16 is going to either sacrifice or blend together certain pixels. Obviously, you can't fit all the pixels into a smaller space. More likely than not, certain 1-pixel wide lines or 1 pixel dots are going to disappear entirely.)
As such, using a tileset designed
specifically to fit your maximum screen resolution will always be preferable to using an oversized tileset... so long as pixel art is used.
In comparison, the details in photos and drawings are usually blending across gradients of colors and shades and so there's a lot more room to blend and interpolate the details using resizing and anti-aliasing techniques. They're
much more forgiving in terms of resizing before important details are lost.
Arclance, I did take a look at your resizing example. And I would agree that Cubic looks the best, with Nearest being a close second.
However, IMO, all of your resizing examples have an unacceptable level of blurriness. I would not be satisfied enough even with the Cubic method to switch to, say, a 24x24 size tileset and use that method to resize to fit my 1280x960 resolution monitor.