Underfire, the differences you quote are interesting.
Is it possible that aircraft systems have different EGPWS software mod states; or are there a differences in actual equipment / manufactures – EGPWS vs T2CAS(TAWS)?
Another alternative is if the navigation procedures have different (even erroneous) coding?
Re special handing; from my ancient experience these were very rare situations and often only temporary until the EGPWS database had the necessary fix. The other extreme was to inhibit the advanced features at certain locations; obvious not favoured. Thus more permanent fixes were sort, provided the EGPWS manufacture was informed of the problem.
If problems are continually encountered ask the manufacturer to investigate; an EGPWS memory download should provide all necessary information – the storage capacity is very large and includes all alerts and the immediately preceding flight paths.