Etymonline contains useful information.
suffix forming verbs, M.E. -isen, from O.Fr. -iser, from L.L. -izare, from Gk. -izein. English picked up the French form, but partially reverted to the correct Greek -z- spelling from late 16c. In Britain, despite the opposition (at least formerly) of OED, Encyclopaedia Britannica, the “Times of London,” and Fowler, -ise remains dominant. Fowler thinks this is to avoid the difficulty of remembering the short list of common words not from Greek which must be spelled with an -s- (e.g. advertise, devise, surprise).
That last list includes compromise too, as that does not have a Greek root.
The one I’ve had most contact with is baptise/baptize which comes directly from the Greek baptizein and presumably should be spelled with z.
As someone with an interest in letterforms, I've always found z an anomalous letter (the thick stroke goes in the wrong direction) and I far prefer the appearance of these words spelled with an s. That may also be a contributory factor (as well as Fowler’s “difficulty”), even if only subliminally.