[quoteSo] i'm wondering if there is a de facto proof about the difficulty levels.[/quote]

You can test it yourself. Just fire up custom battle and make a fight on even ground between two identical units. Look what happens on different diff levels.

Just take note that in some RTW version Custom battle difficulty didnt work ( I dont remember on what version ).

But it works on campagne map. I used to play H battles but I switched to M now and difference is very noticeable.
Battles are just to easy so I use General Camera. It really increases difficulty of big battles.