关心: be concerned with, show solicitude for, be interested in, care for, regard
双方共同关心的问题 matters of interest to both sides
互相关心 care for each other
关心 is generally used in daily life.
关怀: show solicitude for, show loving case for
向...表示最亲切的关怀 show the warmest solicitude for...
祖国人民对海外同胞深为关怀 The Chinese residents overseas are much in the thoughts of the people at home.
关怀 is generally used in politics.