I haven't owned a Honda City, but Swift is anything but Fuel efficient. It does have a powerful engine and is otherwise a durable car with easy maintenance.
Since they both fall in the same tax bracket, you have to consider whether you want a compact hatchback or a sedan.
Although Suzuki is know for ground clearance but I am not particularly happy with Swift which tends to dip with 5 people seated. Nevertheless comfort and space are a plus on City coupled with fuel economy. But price and earlier availability is another consideration too. If you can afford to, go for a city, otherwise swift ain't a bad option either