It can save money and space. Dual band antenna can be realized with the dimensions of single band antenna only. It may take little higher dimensions. Moreover, if the two bands are not used at a time in any case then dual band antenna is far better than single band antenna.
The dual band antenna can be designed to occupy less than half the space needed for two single antennas. Thus cost and space can be reduced when using dual band antennas.
In some cases of antenna design, space management is very important in addition to cost cutting. Dual band antennas can be fabricated with much less footprint area compared to two different antennas at required frequencies if properly designed. In some cases, device might need to transmit/receive over any of two bands time to time but not simultaneously; then, a dual band antenna plays an important role.