The Elantra 1.6 international fuel economy numbers don't look too good. 6 speed auto should be more fun to drive but CVT will definitely be more efficient. Plus the power difference between city 1.5 and Elantra/corolla 1.6 is barely 6hp, but the weight difference is around 200-300kgs.
I once drove Elantra 2.0 and yeah it was definitely faster than my 1.5 CVT city, but the difference wasn't that big. Plus the transmission felt less responsive on kickdown than the CVT. I'm pretty sure Elantra 1.6 will be slower and corolla 1.6 is definitely slower as seen in YouTube vids.
City has another advantage of more legroom in the back compared to Elantra. Elantra 1.6 and corolla 1.6 are too feature barren, they don't even have cruise control and I think not even retractable mirrors.
At current prices the 1.6s don't make sense at all, imo it's better to either go for aspire or ativ X and get an efficient and well featured car, or go for Elantra 2.0 or corolla 1.8 used for around the same price to get an overall much better car.