On the O.P.'s original request for an idea on what works best I think MM hit the nail on the head when he said thinness in a chopper can actually assist in "biting deeply" into the wood. My Hossum 12 inch Retribution/Machete combo knife at 3/16th thick ties or eclipses my NMFBM in some comparison use I have done recently...it took a while though for me to get the handle on the Retribution just right otherwise this would have been noticed sooner...the handle needed rounding a bit on the spine as the edges there were catching a nerve in the web of my hand...but for a knife weighing 20oz's and the other 30oz's that is quite an achievement. So for me thickness is no great advantage here unless you need some prying ability as well and if so then fine....you are better off with a thicker knife.

However to me a prybar is the right tool for this task....not my knife.

For batoning it is the depth of the blade and a twist of the wrist which finally opens up the log...so long as you don't try this too early thickness does'nt matter.

For stabbing a thinner blade is much preferred....thicker just offers more resistance and once stuck in....if you then go to open up the stab entry to a cut...to eviserate for example...thinner is much easier to pull through. You don't see many Butcher's using .25+ knives...usually they are 1/8 inch or 3/16 inch maximum.

The only advantage of thickness in my usage which is fairly well rounded is on the surface area for the Baton to hit...a thinner knife or one with a swedge will bite into the Baton...but in my experience there is no real performance difference if this happens and the Baton if selected right still works fine.

However you need to find a "thin" large knife made from the right "steel" by the right person who knows their craft....personally I would love to see Jerry or Dan do a 3/16th Bolo/Machete style blade...but it is perhaps the "marketing" fears that some idiot will then Noss test it by hammering it into a tree and bouncing on it "snap it" that stops these useful designs from being done...I don't know...but for sure the "thinner" knives are where the "user advantage" is
....but the bad press from a broken blade might put them off.

Personally it would not put off me or many here who try to use their knives and learn what would make them better....most of us already have belt sanders to re-profile edges....the next phase is to re-profile the whole blade to a useful "convex" grind....read Horn Dog's comparison tests and you will soon see how the best performers are often the ones which have been modified the most.