The AWG definitely has advantages. It can go to higher power (about +24 dBm), lower frequency, generate more interesting modulations, and create signals other than a sine. It also probably has a more accurate output power, especially when performing modulation.
The two instruments have similarly specified harmonic distortion (-30 vs -32 dBc), but my feeling is that the 8656B would be slightly better. For small signals, the AWG probably has a lot of quantization-noise.
The frequency reference in the 8656B would be much better, within a few ppm per year drift. The SDG100 is +/-100 ppm per year. However, this could be easily rectified with an external reference. And, if you care about your frequency, you should be using a more accurate reference (like a GPS-DO, or OCXO).
Another big advantage of the siggen is its dynamic range. It can go down to -127 dBm. The AWG can only go down to -50 dBm.
I've never done receiver alignment, but I think that your major issue would be the frequency accuracy. However, for either instrument, you probably would need an external reference (unless you have the high-stability timebase option 001 for the 8656B).
That being said, I'm in the market for a siggen (I need up to 128 MHz), in case you're selling. [I'm in Indiana]