It was important for me to outdo them, to feel better than they were. [VERB noun]

超过他们，感到自己比他们更优秀，这点对我来说很重要。

Both sides have tried to outdo each other to show how tough they can be. [VERB noun]

双方各不相让，都想显示自己有多么厉害。

Not to be outdone, the Croats came up with a peacekeeping proposal of their own.

克罗地亚不甘人后，提出了他们自己的维和方案。

She wore a lovely tiara but the groom, not to be outdone, had on a very smart embroidered waistcoat.

她戴了一顶漂亮的冕状头饰，而新郎也毫不逊色，身着一件非常讲究的刺绣西服马甲。