Modern Diesels have some other tech to help lower the NOx levels (like EGR and SCR systems) but the main problems are that older cars didn't have such systems, plus, for many years, VW lied and faked data, partly to avoid having to implement SCR (saving thousands per car, and the re-engineering) and partly to say the cars were cleaner than they were.

Moden SCR systems (they inject DEF, aka, urea, into the exhaust) do a really good job getting rid of NOx.