My son has offers from both schools. Clearly, we won't know till their first A-level results what their outcomes are like, but as another poster said, your child is likely to do very well at any of these maths schools. The established ones like KCLMS, Exeter and Liverpool, all score highly on value add/progress scores post-16.
IMHO, there are some differences to consider though, such as:
If you want to do a 4th A level, CMS offers CS as standard. ICLMS gives you wider options of doing so with Woodhouse College next door. Computer Science, Music and Economics are the most popular choices there for the ICLMS students.
CMS has a smaller intake of 40-50 students which makes it feel a small school. ICLMS has 70 students per year and again with the Woodhouse link, this might provide the feel of a larger school with the associated extra-curricular activities available
CMS is close to the train station but in my experience, the train service is not the most reliable at times. I used to commute there by train but one advantage was the trains out from London were not too busy, so you could normally get a seat and work if you want.
Depending on where you live, ICLMS may need a bus for part of the journey which increases the risk of delays if also using train/tube.
ICLMS seems more geared up towards engineering than CMS. CMS seems better geared up for Computer Science with links to the large tech company cluster in the city plus they seem to do well in Physics – they had quite a lot of students win gold awards at the recent Physics Olympiad.
One thing that really stood out for my son with CMS was they seem to have a more flexible learning structure based on an individual pupil’s needs compared to ICLMS or KCLMS. E.g. your tutor might suggest doing some other project work instead of coming to the math lessons for a week. CMS also have a lot of flexibility in their problem solving sessions, so more able pupils can do the harder questions. I believe KCLMS do this too, but they have a kind of streaming into top, middle and lower streams.
Good luck in your child’s decision!