get the better of 打败, 战胜,在...中占上风
He got the better of his rival.
他挫败了他的对手.
He tried to get the better of his sleepiness.
他试图克服自己的睡意.
My curiosity got the better of me.
我克制不住自己的好奇心.
get the best of 战胜,使屈服；在（斗殴中）...占上风
get the best of an opponent 打败对手
My anger got the best of me. 我抑制不住而发火了.
再看
get the better of/best of
win over； beat ；defeat 赢得；打败；获胜
*He got the best of it in the contest．他在比赛中赢了.
*Be careful in dealing with him because he will try to get the better of you．对付他要小心,因为他会设法击败你.
*He easily got the better of her in that argument．在那场辩论中他轻而易举地击败了她.
===结论：虽然楼主很有心,但是这两个词组在两两比较时使用没有区别.但是如果对手是多人,则用the best为好.
===供楼主参考.