Hi,
it's depending on the type of antenna. Antennas in resonance (e.g. dipole, patch...)are usually narrow, antennas that are not resonant (e.g. Vivaldi, spiral antenna) are broadband.
The size influences the bandwidth as well e.g. if you shorten a dipol and match it with a coil it get pretty narrow in bw. Use very thin material for antennas make them narrow, very thick material makes them broadband.
...there are many differences and no general rule... really depends on the type.
Ciao, Bodo