The Bartimaeus Trilogy is being published by 38 different publishers around the world, and there is a lot of variation in the cover illustrations used.
I think the series is quite difficult to illustrate successfully, partly because fantasy is a difficult genre to get right (since everyone will have different ideas about how, for instance, a djinni looks), and partly because fantasy is only one of the elements of the trilogy. There's also plenty of humour, politics, adventure, a little horror, some history… Each cover must aim to balance some of these elements, thereby summing up the appeal of the book.
There's also the question of age-range. I'd like these books to be read by all ages, so an ideal cover is one that doesn't seem too young or too adult.
As an author I get some input into the look of the UK and US editions, but ultimately the decision has to be made by the publisher. Other countries have to aim to pitch their editions at their own markets, which makes for a lot of variety.
Here are some international editions of the Bartimaeus Trilogy: