both of them mean "defeat"
击败 is used when u defeat a single people or an army.
击溃 is used when u defeat an army.
败 means lose whereas 溃 means 分散、散开 of lots of water
a troop is always stay in line, do things in order etc. everything is in order. but when they lose and run for their lives, nothing is in order. this case is called 溃---because a troop is just like some water. when they lose and escape, it just likes lots of water separated. for example, when a dam is broken, u gonna see 溃.
this is why 击溃 is only used for a troop.
there is another character: 崩
崩 describes the case that a mountain is breaking. as u know there is a 成语：山崩地裂
this character can be used when we describe a system is breaking.
there is a word: 崩溃
we can say a system 崩溃了, or a person 崩溃了. for example, a person get lots of bad information at a short time, he gonna 崩溃. if some powerful virus is in ur computer, maybe the system of ur computer gonna 崩溃-----系统崩溃
another word: 溃退
when a troop lose and retreat, we can use this word.
for example, 敌军溃退了。
we can also use it for waterflood. for example, 洪水溃退了.
we can see 溃退 and 击溃 are similar.
敌军被击溃了 = 敌军溃退了
溃退 highlights that a troop retreats because there is the character 退(back)
anyway, 溃 means lots of same things were in order and suddenly the order is totally broken, so things are totally separated and no order.
i hope that u know these words now: 击败 击溃 溃退 and 崩溃.