Better to eliminate a Civ completely or leave them one city?

[Ansive]

Sometimes it is worth leaving them alive. Even if you haven't met a lot of civs.
For example if you have too much land (that you don't plan to settle) and a religion that needs followers or cities.
You might also get some trading routes from them if they have no other good trading targets.

Better to have the land settled by a crippled civ than a faraway friend or enemy.

But yes, the trade off is being denounced and spied on.
It's very hard to be friendly with a civ after you take their capital.

 

[Callonia]

Generally I'd rather just apply the coup de grace myself. I get to hear the lamentations from my hated foes. And it removes their spies + Diplomacy + And allied status to any city states until they're resurrected.

And if you do it right, you could just conquer 3/4 of the world and the AI will be rooting you on, as long as you're friends with right ideologies.

Plus you get to know who your true friends is. If the AI was your friend until nearing the end of game.. he was a true friend. Hold no grudges.

 

[belligerent]

I usually leave a city up for most civs. It gives the other remaining warmongers weak fodder to focus on. Often, they'll go march/sail an army to the weakling and you can roll in behind and commit the oldest sins in the newest ways while a good portion of their army/navy try to scramble back... then you just pick them off as they return.

Any time I can split opposing forces, I do it, and having weaklings lying about makes that easier.

 

[miaasma]

if i care about diplomacy i'll leave them on some useless city they shouldn't have founded

as the game drags on though you tend to rely less on diplomacy for trades with ideologies in play. so if it suits me and i'm starting to not care about burning bridges i'll eliminate them