The validity of the argument depends on context. Sometimes it is: "sorry, I can't help you now, because all my resources go to higher-priority cases". Sometimes it is: "meh, I don't care... but I can use a comparison with this other case (that I am not really contributing to) to make you seem pathetic".

In other words, if someone says: "I don't care about your problems, the children in Africa have it worse", and the person does contribute to a charity for African children, then the response is valid (although we could discuss the optimum way to say the same message).

If someone says: "I don't care about your problems, the children in Africa have it worse", and the person does nothing to help children in Africa (or anyone else), then it's just a convenient excuse and a move to gain relative status at the other person's expense.