I think this is more of a scientific than a historical question. Garbage smells because organic material is decaying. Bacteria produce the malodorous gasses, which seem to smell the same all over the world today. So most likely the same bacteria would be decomposing the same organics (e.g. food waste), generating the same gasses and therefore the same smells.

Rotting organic matter has always smelled the same. If you mean the stink of a city in general then no. Cities smell pretty dam good these days in comparison to a 19th century city filled with horses shitting everywhere. And Victorian London smelled a lot better after the construction of the sewage system. Before the city was filled with cease pits (i.e. holes in the ground for poop) that needed clearing out every once in a while. Rivers smelled petty horrid in the past to. People used to just dump raw sewage into rivers! The Seine and the Themes stank! The Themes got so bad in the summer of 1854 that it's still called the Great Stink! This incidentally was the impetus behind the construction of the London Sewage system.