Is donating to the needy during famines better than performing Umrah in Ramadan?

Yes, charity given during times of need and severe famine is better than a voluntary 'umrah (definition), because the benefit of 'umrah is limited to its performer, whereas the benefit of charity given to the needy and the hungry extends to others. That which has an extended benefit is better than that which has a limited benefit. This applies to poor Muslims everywhere, with priority given to the poor within one's own country over those abroad.