Not too much difference, just like "at once" and "immediately" in English. 立即 is a bit more formal than 立刻。

两者并无明显区别。 ※补充：立即=马上=立刻=即时=随即=速即(不常用)=立时(不常用) If you like my answer, please click the like button on our Facebook Fanpage. https://www.facebook.com/cceg2017/ Thank you :)