The difference in pronounciation is not huge but still important.
In Danish we would pronounce the ending vowels more stressed than you probably would in English e.g. in Christine the "e" sound would get sort of "sucked up" by the "n" sound. Yet, I think you will get very close or at least get a very good idea of how the names would differ in pronounciation by first saying the name Christine as you normally would and then right after say either the vowel "e" or "a"
Of course there is also something about the general rhythm of a language where English and Danish is different here and there and that could influence the way the two names are spoken too, but that is too hard to explain for me in text only. Yet, the above described is the core of the matter and should give you a good idea I think.