I'd say usually better quality rather than definitely better quality. While the Lanczos filter is always superior to the box filter in theory, there are some case in practice where the box filter may be better.
If you're downsampling a line-art image, for example, you may actually be better off with some variation of the box filter. The negative lobes on the Lanczos filter can induce objectionable ringing because line-art tends to be full of what are basically step functions. It's a similar issue as with strong mosquito artifacts on JPEG compressed line-art.
A filter function that is everywhere non-negative, such as the box filter or a Gaussian can't suffer from this problem. Of the two, the box filter will give you sharper results but of course it doesn't antialias as well, either.
If you're downsampling a line-art image, for example, you may actually be better off with some variation of the box filter. The negative lobes on the Lanczos filter can induce objectionable ringing because line-art tends to be full of what are basically step functions. It's a similar issue as with strong mosquito artifacts on JPEG compressed line-art.
A filter function that is everywhere non-negative, such as the box filter or a Gaussian can't suffer from this problem. Of the two, the box filter will give you sharper results but of course it doesn't antialias as well, either.