Antibiotic resistance provides evolutionary rescue for bacterial populations under the threat of extinction through antibiotics. It can arise de novo through mutation in the population, or be obtained from other bacterial populations via the transfer of a resistance-conferring plasmid. We use stochastic modelling methods to establish whether the most likely source of rescue is via a plasmid or via the chromosome, and show that contrary to what is assumed plasmids are not necessarily beneficial locations for resistance genes. Competition at the plasmid level of selection is of great importance - the spread of a resistant plasmid in the population can be slowed or entirely stopped by a non-resistant version of the same plasmid. We suggest that future studies on antibiotic-resistant plasmids should explicitly consider competition at this level of selection.