The fast path is for most languages where the text glyphs are placed in order. The complex path is for languages where the shape and size of a glyph depends on the characters around it. For example, Arabic text or Thai text would go through the complex code path. There are some other cases where the complex text path is used (I think "text-rendering: optimizeLegibility" forces the complex text path).

In Safari and most of the time on Chromium Mac, the complex code path is handled by CoreText. In other Chromium ports and on Blackberry, complex text is handled by Harfbuzz-NG, which is also used by Firefox.