Si and Ga based compounds are not really competing but rather complementary.
The problem of these semiconductor compounds is that each compound has a sweet spot and band of frequency operation and they're all different from each other. Perhaps all the advertisements and marketing never tell you that the disadvantage of AESA is that its frequency band for a particular AESA is actually limited by the semiconductor substrate material used by the emitters of that AESA.
For example, GaN and GaAs works best at around the X-band (8 to 12GHz) but if you want to work with higher frequency like Ku band (12 to 18 GHz), its better to use Indium Phosphate (InP) or Silicon Germanium (SiGe). And if want to work with lower frequency like S or C band, Silicon or Silicon Carbide is better.
Likewise, Silicon or Silicon Carbide isn't probably what you want for an X-band emitter. But it works for communication frequencies (800Khz to 1.9GHz), or for S-band (2 to 4GHz).
So let's say a fighter radar that uses high frequency X-band, you might want to use GaN. Another application might be an SAM fire control radar using X-band for missile target illumination. But if you want a radar for SAM search and tracking, with lower frequency like in the S to C band, you might want to use Silicon Carbide instead.
Note, Raytheon's new generation SPY-2 uses a dual array setup. Its not hard to figure out why from the above.