First and foremost, it's a wrong notion that Kaizen is a rapid improvement technique. Kaizen means Continuous Improvement, which means it's a journey and not a destination. Kaizen is not a specific tool, rather it's a mindset of Continuous Improvement. Kaizen helps to identify all the 3Mu's (Muda, Mura & Muri) and improves all aspects of a business through process standardization, efficiency increase and waste elimination.
The fallacy created about Kaizen being rapid improvement technique, stems from the feature of Kaizen - big results come from countless small changes which are accumulated over time. This actually means that everyone is involved in making improvement.
Classic example of Kaizens can be transformational projects taken by Senior Management, conducted by a cross-functional team, which aims at improving all the functions & aspects of overall business of an organization.
DMAIC, which is one of the tools under Six Sigma, primarily focussing on Mura (variation/inconsistency). Thus DMAIC focusses on improving the quality of final outcome by finding and eliminating causes of defects due variances in the business process.
Conclusion -
If variation in the process needs to be curtailed then DMAIC / DMADV can be used.
If complete business process transformation / mindset change is needed, then Kaizen approach is useful.