After using both I can say I will stick to the Zenfone 6.
The build quality and design is better, very premium feel.
In comparison, the redmi note while a good build, feels more plasticky and cheap.
as quoted from BESERK1980:
Agree on that part. Especially when you use the Audio Wizard Music Mode, the sound quality is a LOT better than the redmi note. The redmi note audio output is... meh.
Back Camera quality on the Zenfone 6 is WAY better, the redmi note back camera is really just not good, noisy even in daylight.
The signal reception for both mobile and wifi is better on the Zenfone 6. At places where its usually a weak signal for the Note, i get full or nearly full reception on my Zenfone 6.
Support for SDXC 64GB. The redmi note only supports up to 32GB.
Performance is really on par or better, the Zen UI feels more fluid than the Redmi Note MIUI. Most of the time when web browsing, I think the Zenfone seems smoother.
Redmi Note, thanks to MIU,I has this really annoying issue for me that the whatsapp get pushed to phone late by mins or even hours!

No such issues with the Zenfone 6.
I travel a lot, so the dual sim slot is good for me as I don't need to bring 2 phones and both sims can be active at the same time. Both slots are 3G slots btw