I found this at hdtvprimer.com:
When two identical antennas are mounted together (ganged) and pointed in the same direction and wired together properly, there is a theoretical possibility of a 3 dB improvement. That is, twice the signal power is delivered to the TV compared to what a single antenna would do. In practice, 2.5 dB is readily achieved, 0.5 dB being the typical loss in the combining device. But if the two antennas are pointed in different directions (towards different stations) a 3.5 dB loss for each antenna is the likely result.
The above statements are true regardless of whether the antennas have shared or separate amplifiers. For a shared amplifier, if the antennas point in different directions, half the power each antenna takes in reflects off the combiner and is rebroadcast out the antennas. Why this doesnâ€™t happen when they are pointed the same way is harder to explain.
For dual amplifiers, when the antennas are pointed the same way, this signal is increased by 6 dB but the noise is increased by 3 dB, so the overall improvement is still 3 dB. When they are pointed differently, the 3 dB noise increase causes a signal/noise ratio loss of 3 dB for both stations. Dual amplifiers will eliminate the combiner loss, but only if the amplifiers are closely gain-matched.
(Ganging non-identical antennas is not recommended. They would need to produce equal voltages, and adjusting out the phase difference might not be possible for all stations.)