I haven`t met anyone who has been studying at either LSI or Central of English. So I only can provide u two some points of my view as follows:
1. Both schools are located in the busiest street in central london. Therefore the environment is a good place for studying. If u love shopping after morning course, both schools will be the best choice though.
2. Secondly, u will suffer from traffic jams or u might find it very annoying when u need to use the tube to travel to ur school during the peak time.
I have heard people saying that the "International House London" is a quality choice but the price won`t come cheaply.
Anyway, hope the above-mentioned suggestions do help and wish u two a happy trip~ godspeed~