Downsizing is important for fuel economy, but don't think BMW is making a compromise on performance. The 1.2-liter actually has more power than the old 1.6, 102 hp available from 4,250rpm, as well as 180 Nm of torque. This means it's got a little less power and a bit more torque than the Audi A1 1.2 TFSI, which is OK.
Performance wise, the new One gets from 0 to 100 km/h in 9.9 seconds with a manual or 10.2 with an automatic, while to speed is a very respectable 195 km/h whichever gearbox you go for. Average fuel consumption is around 4.6 L/100km with a manual or 4.8 with the auto. Again, this is on par with the Audi A1.
We don't actually have photos of the One yet and it's not available to buy, but expect fewer pieces of trim, no fog lights and a slightly more spartan interior. Only question is, will the Countryman One also get the 1.2-liter as well?