I don't know much about the British School but believe it is owned and operated by a larger language school company (ACS). I have never heard any feedback about it (good or bad). I don't believe they accept children as young as 4. Their curriculum begins at the first grade level.
Geneva English School has quite a good reputation, however. It is a friendly little school on nice grounds. Parents seem quite happy with the quality of the teaching and the school atmosphere. The fees are on the upper-end though.
There are several English-language play groups and external extracurricular English school/classes which may meet the needs of your 4 year-old and be less damaging to your wallet than enrolment in private school. For example, you may want to check out Dynamic Learning (www.dynamic-learning.ch) or the Interactive Learning Centre (www.interactive-language.ch). In addition you may also consider enroling her in the Swiss public school system (1/2 days are possible). This is free and she could benefit from submersion into the French language. Just my opinion. Lastly, if you truly want an English-language nursery/pre-school I suggest looking at Bell Nursery (http://www.bell-school.ch/en/General/index.php).
Good luck on the move.