Acclimate is an older word, apparently, held onto by Americans while in Britain, Australia and New Zealand (etc) we moved on and acclimatise has long been preferred. Think too of Fall And Autumn - in Britain we stopped saying Fall centuries ago, but Americans stuck with it. To my ears, acclimate sounds clunky, but that could be because I'm more used to the British English version. Also, aesthetically, acclimatise sounds more agreeable to my ears.