How useful is double-glazed glass for sound and heat insulation in a semi-tropical climate?
The important comparison is not between double glazed and single glazed windows. It is between specific windows and their specifications because there are high quality single glazed windows and low quality double glazed windows and even among one group or the other, thermal and acoustical performance can vary with manufacturer and part number.

Generally speaking and so long as the sash is not open, double glazed windows will offer superior thermal performance because the separated panes inhibit heat transfer by conduction. As a relatively mature product with several decades of manufacturing and installation history, seal failure that allows the dissipation of the inert gas is not usually a problem with products from established manufacturers.

The American Architectural Manufacturers Association has well established standards for windows and doors. The Window and Door Manufacturers Association is another resource. Their building science is sound. Similar resources exist in other regions.