Within this budget, you can buy either of them but the question remains, what your requirement is! comparing both of them is like comparing apples with oranges.
If you want a small hatchback with a powerful engine, then I would say Cuore 2004-5. Even here you have two options, either Automatic or Manual. You can buy the 2006-7 model in this price range. I have one, and it's not an under power car better than Mehran and Cultus when it comes to body and engine.
But if you are looking forward to having a compact sedan, the City 2000-2002 should be chosen, though I think you have to increase your budget up to 6 lacs. Bear in mind that City maintenance is expensive and parts are not cheap. But if maintenance cost is not an issue, then it is still a better-looking car.
Finally, when it comes to fuel consumption, too much of your surprise, Cuore and City both have almost similar fuel average, believe it or not. The reason behind City's success has always been its fuel average which is 11-13 Kmph and Cuore would give you 12-15 km.
Now the choice is obviously yours.
Best of luck 
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