Analising the kanji of booth you can see that in 運命 has the kanji 運 which has the meaning of fate, but also can be interpreted as luck, advance, followed by the kanji 命 that means life. With that said you can see it as you luck in life, or how you progress in life, but that's only an interpretation. The other one 宿命 has the kanji 宿 which means residence, reside, therefore you can see that word as your place in life. Usually the last one (宿命) has a negative meaning, it's most used in phrases referring to a disaster. So I would recommend you to use 運命.
Also, I don't know if you are interested or if that is your intention, but in Japanese/Chinese folklore they have a concept of 赤い糸 which represents the predestination of love.