The reason that higher ABV, pot distilled, liquors change in the cask is by extraction of flavones, tannins and other materials (let's keep column distilled alcohols out of the discussion). Evaporation and wicking can happen (angel's share), but these phenomena will not normally mellow the liquor (the opposite can be argued, higher concentration of organics will tend to harshen the beverage). Also, some of the congeners will mellow due to the charred nature of the barrel (adsorption onto the carbon surface). The porous nature of the wood will also act as ion exchange column, trapping some of the less than desirable compounds.
Modern bottle glass is very non-reactive and non-porous. The only bottle aging that I have heard that bears some validity involves some forms of short aged Mezcal (less than 50 days in the cask). However, that is most likely due to extractables that had not had adequate time to complete reaction in the cask. Material that has spent years in the cask has pretty much gone to completion pre-bottling.
There are some who believe in bottle aging. I have seen neither proof of this (not a pun) nor a convincing mechanism for this to occur.
My bet is that if did a double blind experiment where I took 10 samples of whiskey that was "bottle aged" for 20 years and took 10 samples of the same spirit, each from a different production year (thus, bottles aged form 1-10 years), a whiskey taster with a developed palate would not be able to identify which were which. There will be variation due to the nature of natural products, but there would be no definitive correlation between bottle aging and flavor perception.
I am sure that if I repeated the experiment in a non-blind condition, then you would see bias.