Couple of things to watch with the KLM flights via AMS:
- the cheapest fares shown usually book into the economy light fare bucket which is hand baggage only. The other fare types can be selected when booking.
- Some of the cheaper fares involve an overnight at AMS at your own expense.
Savings can also be had on KLM where there is an extra sector via CDG so instead of XXX-AMS-KIX you route XXX-AMS-CDG-KIX.
OP is Dutch, I’d assumed they would start from AMS, not route through AMS.