Very Hard campaign difficulty makes the AI homicidally agressive, sharing a border means you WILL be attacked by them, no matter your relations to them, alliances, or etc. This is absolutely no fun at all IMO, and unless you want to be constantly fighting battles turn after turn, you'd probably want to use the "Force Diplomacy" minimod to enjoy this setting.

Hard is what I usually play on, the AI seems to do fine money wise (is able to field large armies, seems aggressive enough, tends to actually garrison its cities, etc) and is nowhere near as insanely agressive, although it still tends to be stubborn toward ceasefires.

No idea about medium.

Since you mentioned the Alex.exe, I've heard the Medium difficulty there IS supposed to be similar to harder settings in RTW/BI.exe. I'm using Alex now on Hard, and it's been fun so far. The AI is actually somewhat capable on the strategic map, is building large, balanced armies and actually combining them before attacking. Battle AI is still dumb as a brick, thanks to the hard coded limits of RTW.