The .bin and .hqx file formats — what's the difference?

When downloading files, you might be given a choice of two different file formats, MacBinary (.bin) or BinHex (.hqx).

What's the difference between these two file formats? A .bin file is typically smaller than an .hqx file, but is less compatible with earlier Macintosh systems, such as Mac OS 7.0, 8.0, and 8.5. An .hqx file is typically larger, but is more compatible with earlier systems.