1

Does it mean the same thing? If not so, then how to say that I am better than her.

I'm out of your league

You are out of my league

2

No, they do not mean or imply the same thing.

It is a sporting reference often used as an analogy. Professional sports tournaments are normally organised into leagues, pitting similarly performing teams against one another. When a team reaches the very top of a league, they may be promoted to the next league up; likewise, when they hit the bottom, they may be demoted/relegated.

In the context of dating, "out of one's league" idiomatically means that a person is superior to you and would not be interested in dating someone who was not at a similar level. It could be applied to degrees of perceived beauty, social status, class, or intelligence.

If someone said "she's out of your league", it would imply that you are not good enough to date that person, for whatever perceived reason.

Your examples are a little different, as they appear to be said to the person they are also about. Saying "you are out of my league" would be a compliment of sorts, but is also self-deprecating. I imagine one would say that in the hope that the other person says "no you're not" and then they live happily ever after.

"I'm out of your league" would be a vain boast - saying that you are better than someone else and that they are not worth dating.

The expression is also used in other figurative contexts - for example when comparing hardware (eg you cannot compare these two cars - one is out of the other's league!)

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