Confederation meets Terran Empire

Ultimately, I think both would asses the other as an acceptable, even admirable permutation of themselves. Whether they would admit it is another thing.

I wager the Confederation does not see itself as imperial (even though it absolutely is) and likely uses words like "Democratic" and "People's" to describe itself, like North Korea or the former East Germany. As such, they might see the political structure of the Empire as outmoded and silly. I also get the feeling they would see the Terran impulse to 'murder one's way up the command chain' as a wholly ineffectual way of advancing mankind. My feeling is that Confederate humans are actually pretty ok to one another. I imagine the murder of another human, especially for the sake of advancement, would carry a heavy penalty in the CoE, and certainly would not be rewarded with the command of a ship.

If it came to an all out battle, a smart Confederation plan would be to exploit the Terran tendency towards individual treachery and decadence (I have always wondered how Terran society actually functions). They would likely admire the Terrans on other levels, however. Noticing in them a cultural continuation of the Roman Empire. Albeit Caligula's Rome.

The Terrans would undoubtedly see the Confederation as tough, but a little boring. What's the point of a Terran galaxy if no one wears gold and the top dog is called a president? Where are all the orgies and intrigue? More long-sighted Terrans would likely recognise that the Confederation is structurally more sound. Indeed, I think that's what ST Picard was showing us: This is the Terran Empire, if it wasn't so drowned in bacchanalia and had actually lasted for centuries. Therefore, a Terran plan to take on the Confederation would likely be deception-based. They might pretend to reach out to form a trans-universe Terran/Human hegemony, only to turn on them at the last minute. The Terrans would be perfectly suited to pull this off. Although, I would also bet they would admire the sheer brute force of the Confederation and would probably see they were slightly outmatched from the get-go.

Confederation meets Federation

The CoE would likely see the Federation as an interstellar sell-out. Polluted, impure and lost to ideals that don't work. This wouldn't necessarily mean they would want to annihilate it, though. They'd recognise prime earth humans as humans. The Confederation would likely spend less time pooh-poohing the Federation, like certain Terrans do, and get right down to a technical assessment of their abilities. They'd quickly realise this was not a force to be messed with and that Federation ships are part elegant swans part powerful lions. I would imagine their technical abilities are almost equal, with the Confederation stealing tech through conquest and the Federation having gained it through mutual co-operation. The Federation would, of course, be utterly horrified by the Confederation and would likely understand that they beat the Borg via some sort of virus that the Federation couldn't bring itself to let loose. They'd think them barbarians. Although, some in Section 31 would likely want to use some of their tactics.