Here is a way of looking at the flaw in using Dawes or Rayleigh limits to discuss the amount of detail/contrast transfer in telescopes.
Regarding the in focus diffraction pattern of a star. There's a central disc of light, then a dark 'ring' - the first minimum - and then the first bright ring, a second minimum, a second (much fainter) maximum and so on.....
The radius, in arc seconds, to that first minimum is 138/D where D is aperture in millimetres..
To the first ring the radius is 163/D, (telescopoptics.net) These numbers are a few percent smaller for increasingly obstructed scopes but for this discussion we will stay with unobstructed....Also let's assume a fairly ordinary star of around 6th magnitude where the second bright ring is too dim to see...
Imagine your 150mm scope is showing a beautiful, motionless first ring on a night of good seeing at 300x or so.
The first minimum is at a radius of 138/150 = 0.92" and the first ring is at a radius of 163/150 = 1.09". These numbers differ by only 0.17", the dark space (depends on the brightness of the star) is, at most about 0.3" across. Yet you can clearly see it....if seeing allows.
This must mean that the 'balls of confusion' are only about o.3" or a bit less in size, allowing you to see the diffraction pattern in all its glory in your 150mm scope. At lower magnifications views will be 'sharper' and the views will be 'tighter' or more 'refractor-like' or whatever non-empirical descriptors you care to use... Your 6-inch scope will perform to its resolution capability and deliver its very best contrast transfer in this scenario...
Now crunch these same numbers for a 16-inch scope. 400mm of aperture, so, first minimum will be at 0.35" and the first ring will be at 0.41" which differ by only about 0.06" now and the black space between the disc and the ring will be barely 0.1".
On the same night assuming the same approx 'balls of confusion' of about 0.3" the diffraction pattern,disc, dark space and ring will be smeared by the atmosphere into speckles or a fuzzball. No diffraction pattern for you! The scope will not perform to its resolution capability nor achieve its best contrast transfer...
BUT....
The radius of this fuzzball in the 16-inch will be approximately 0.7" (radius to first ring of 0.41" plus about 0.3" of 'confusion').
The bigger scope will still out-resolve and out-contrast-transfer more detail than the 6-incher!! Even when you cannot see the diffraction pattern of stars in the 16-incher...
Now all of the above are for a night of decent seeing where a 6-incher can clearly see its diffraction ring.
Imagine much bigger 'balls of confusion' such that the 6-incher cannot see its diffraction pattern. Just a fuzz ball maybe 1.0" or 1.5" in size. 'Balls of confusion of 1.0" or even larger..... In this situation the 16-inch won't out-resolve or out-contrast the 6-inch. The bigger scope will just show more detail/speckles in the fuzzball.
The latter scenario plagues most of us on most nights.
The TL;DR of all the above:
On nights of mediocre/poor seeing where the diffraction pattern is completely smeared out in a 6-inch, the 16-inch will have little or no advantage in resolution or contrast transfer. These nights are all too common.
On nights of good/excellent seeing where the diffraction pattern is clearly seen in the 6-inch the 16-inch will still out-resolve and have better contrast transfer than the 6-inch even though the diffraction pattern is not visible. These nights are less common but, at least in my neck of the woods, happen a dozen or so nights a year....
On nights when the diffraction pattern is discernable in a 16-inch there will be glorious viewing for its owner and the 16 will truly 'blow away' the 6 in all categories of viewing.. These nights are exceedingly rare even in the florida Keys and are unknown where I usually observe...
Dave