Both cars are great in their own league but a 1300cc and 1000cc aren't comparable. vitz is auto and 1000cc so for northern areas corolla is recommended but for someone who travels a lot within city, vitz is attractive choice as it will give better fuel economy but the mileage gap won't be very large and auto is easy to drive in city traffic. My friend had 2003 se saloon he bought for 8.5 lack and sold for around same price i think 50k less (in 2018) but the car was very reliable, comfortable and we visited north on this car a lot of times. I must say i was very impressed by the performance and reliability of this car plus it was around 16 years old car so there isn't that tension/nervousness that is there while taking a brand new car to harsh terrains. That car even visited Pak-China border and all i would say is that corolla is a reliable car but i haven't tested vitz that much so may be vitz is that reliable too. comparing to vitz, corolla has a negative side of fuel economy, i think 1, 2 or may be 3 km/liter less. Rest, the choice is yours.
In my opinion:
Fuel economy and ease of driving within city= Vitz
Reliability and performance outside city= Corolla