The difference is in the way they work.
NOD32 use more of heuristics than signatures, Kaspersky is the
other way round.
Heuristics detection will check for patterns of malicious softwares
and flag them. You then decide if it's harmful.
That's why NOD32 is not recommended for those who don't know their
system well, especially those who do a lot of tweaking and coding.
Anything can trigger the heuristics.
Thankfully for Kaspersky, although it relies on signatures, its
detection rates are high, to make up for the lack of heuristics.
That means the chance of catching one virus is low, especially for
those wild spreading ones.
The latest version of Kaspersky now also has heuristics, but it's
still more user-friendly when compared with NOD32. NOD32 is more
technical. Get a trial copy and try configuring it you will see the
difference.
