I'm not here to recommend Civilization series in general: know that it is awesome.
But why do I think Civ V is the best of the series? First of all, the empire building has got more interesting: the boundaries develop now in much more amorphous manner, and much more consideration needs to be paid to the terrain: it is no longer sensible to spam the whole realm full of railroad and mountain chains are important. Also for some strategies having a small empire is sensible and viable, but the upkeep for big empires is not as crippling as in Sid Meier's Civilization IV either.
Various civilizations still have their individual strengths, but much more customisation and differentiation is allowed via social policies. Religions also have now their own gameplay differences.
Since I personally like exploration and building more than warfare, I also think the combat system has become more interesting, requiring now more consideration how to position the troops (and pay attention to the terrain) instead of the old system of just creating a big bunch of troops and moving them against the enemy (or suddenly finding one in your doorstep).
From this comes also the biggest weakness of Civ V: AIs are not particularly good at handling war and are here quite passive: this sometimes leads to situations where halfway through the game it becomes obvious how the game will go, if you have managed to take enough lead you'll probably keep it unchallenged and the endgame can become something of a grind, and if someone else has pulled ahead it is not easy to catch them the other AIs at least won't hinder the leader effectively.
Also the vanilla game itself is not quite as great as it becomes with the expansions. And I can see that someone much more into warfare would prefer e.g. Civ IV over this, but for a more peaceful builder like me this has brought hours of joy and will continue to do so.
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"Extremely unbalanced, lots of detrimental civs and useless units" Yeah especially in multiplayer the lack of balance really shows. i.e. Catapults completely useless, Rationalism tree mandatory
I really like a lot of the changes in the community patch/Vox Populi. The AI is way way more competent here which makes me wonder if Firaxis makes the AI stupid on purpose because they found that more fun in playtesting. I am in the late game on Warlord (usually play on Emperor without mods) and I am in endless war and the AI never runs out of units. Feels like it needs some mechanic to prevent endless stalemates. There's war weariness which is ruining my happiness but the AI does not seem to care.
Game would be better if AI was actually smart. You don't have to have more than like 4-5 troops to defend your city from a full scale invasion because that's how bad the AI is.
Yeah especially in multiplayer the lack of balance really shows. i.e. Catapults completely useless, Rationalism tree mandatory