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My 6 has started doing this just after its 2 year anniversary. I bet it has something to do with battery age as well

Exactly the same for my 2-year old 6.

This can be "fixed" by resetting the battery data on the phone and then letting it completely discharge before charging. I've had it work myself several times (I own two of every model iOS device for app testing purposes).

My 5s does it if I don't recharge it fully.

iPhone 6s seems to have this particular problem

Yes. I deal with this.

If you have an iPhone 6S with this problem you can get it replaced: https://www.apple.com/support/iphone6s-unexpectedshutdown/

It's called an anecdote. I think that's useful in this situation.

My iphone 5 does it. Tends to be around the 20% mark.