Learn English – which one of these sentences is correct

Your two sentences cover the two cases of using negation to say the same thing.

In colloquial American English, you will encounter "She is not poorer than me" or "I am not richer than her." You will also encounter the more grammatically correct "She is not poorer than I" or "I am not richer than she." In these cases, speakers will often also add the correct form of the verb "to be" to the end of the sentence, since English speakers have become uncomfortable with pronouns at the end of a sentence, so "She is not poorer than I am" or "I am not richer than she is."

I bring up the issue of pronoun discomfort because American English speakers now overcorrect usage of "I" vs. "me" in many situations. In positions where "me" should be used, e.g., as the object of a preposition, English speakers will use "I" instead as an attempt to sound grammatically correct. This has become so pervasive that one can assume it will eventually "become" grammatical. See the Wikipedia article on hypercorrection for more details.

You will not be misunderstood if you use either pronoun variant in these example sentences.

Both ways are correct English.

I gave her your number

This is a perfectly fine response, and the slightly less formal of the two.

I gave your number to her

This is a slightly more awkward construction, but is also slightly more formal.

One thing to note is that in some contexts, they can imply that something else has happened since then (especially if you stress the word "gave", e.g. "I gave her your number, it's not my fault she hasn't called!").

There are a couple of other constructions that emphasise the past tense on its own:

I've given her your number (or I have given her your number)

Both of these are perhaps more natural to hear to an English speaker, especially the first one (because "I have" is contracted to "I've"), and can emphasise that you've simply completed the action and given the number.