"-ize" is correct British English. It comes directly from the Greek (-izein) via Latin (-izare) and is the primary form used by the OED and most other British dictionaries, as well as being recommend by the OUP and Fowlers etc. The "-ise" form is from the French derivation (-iser) of the Latin and was rare in any use of English until the twentieth century.
The exception to this rule are words which have not taken "-ize" as a verbal suffix such as "advertise". This is a back-formation from the noun "advertisement" and as such is always spelled with an "s", both in Britain and America.
As for the word "burglarize", it came into the English language in the late nineteenth century a year earlier than "burgle" was first used. At the time both were disapproved of by language scholars but "burgle" was seen as the more vulgar being an irregular verb created as a back-formation from the much older noun "burglar".
Not really sure how the latter became the dominant form in Britain when it was the newer of the two and the poorer use of English, with the addition of the "-ize" suffix being the 'proper' way (if there can be such a thing) to create a verb.
Where they are difference between the common forms of English used in Britain and other countries, especially America, British people tend to assume some kind of faux superiority as though only one form can possibly be correct, and often showing complete ignorance of the etymology of the words and their cultural context.
As such most British people assume that the word "burglar" is derived from "burgle" and ridicule the use of "burglarize" as they believe it to be unnecessarily turning a verb into a noun into a verb.
Finally, the American spelling of "color" is a result of the American teacher Noah Webster who while writing his dictionary decided to eradicate some of the contradictions that had occurred in English. The "-or" suffix was actually correct in Old English, as much as it can be in a time when there were no standardized spellings, having come from the Latin. But from the time of the Norman conquest French began to have a significant impact on the English language, amongst other things transforming the spelling to the "-our" form used today.
One of Webster's dislikes at having to teach from British textbooks was that the English language of the common man had been corrupted by aristocracy, with this being one such example. Just as the American revolution had been about freedom from such institutions and everyone being equal, he saw a need for the same sort of revolution in language to reclaim it for ordinary use.
As a result of this he aimed to tidy up English by standardizing spellings and removing contradictions. Most obviously they was the dropping of the superfluous "u" in the "-our" suffix and correcting the "-re" one to "-er".
Not all of his changes were accepted, such as changing the phonetically highly irregular "neighbour" to "nabor". While due to a similar, though less successful, movement to simply English in British saw others become the normal form in British English, such as dropping the "u" from some words, such as "exterior", or dropping the "k" from words like "musick".
Incidentally another of his changes was the spelling "connection" so that it became formed by the word "connect" with the suffix "-tion", as analogous to words like "inspection". This spelling only gained use in Britain relatively recently replacing the 'correct' British spelling of "connexion", which I seem to be the only person to still use - and I am not that old!
While a lot of people condemn 'Americanisms', they usually do so while using them!
Michael.