The difference is that Civilization's cultural and diplomatic victory conditions are specifically designed to be the asymmetrical victory paths, the ones where a non-dominant empire has the chance to compete on an equal footing. The domination victory is designed to be the military win, one that recognizes tactical superiority over everyone else. Civ5's version of this condition is an example of poor design because it turns into another asymmetrical victory - there's no need to have any kind of military control to win by domination. Just be in the right place at the right time. (Or even do nothing at all.) You can have 20% of the map against the AI's 80% control in a 1 vs 1 duel, and win the game by nuking their capital and walking a unit in for one turn. It's profoundly cheezy and unrealistic. That's not to say that there haven't been equally cheezy wins in past Civ games (Civ3 diplo being a great example), but bad design is still bad design. Poor victory condition design in the past is no reason to forgive continued design mistakes.
The other glaring flaw with this victory condition is that the AI has no understanding of the mechanic whatsoever. They make no extra effort to defend their capital at all, and treat it just like any other city, when the game mechanics do not value the capitals as such. The human player knows that this is not the case, and gets a giant advantage in the process. It's like setting up a scavenger hunt and then having a giant, glowing neon sign pointing to the objective... when one of the two competitors is blind. The human knows to value the capitals and can work to pick them off. The AI will never, ever do the same. That's why it's a poorly designed mechanic.
The other glaring flaw with this victory condition is that the AI has no understanding of the mechanic whatsoever. They make no extra effort to defend their capital at all, and treat it just like any other city, when the game mechanics do not value the capitals as such. The human player knows that this is not the case, and gets a giant advantage in the process. It's like setting up a scavenger hunt and then having a giant, glowing neon sign pointing to the objective... when one of the two competitors is blind. The human knows to value the capitals and can work to pick them off. The AI will never, ever do the same. That's why it's a poorly designed mechanic.