I’d reach out to Yamamoto to see which Pre they recommend pairing with your amplifier. Synergy should be great with both but they may have designed one of them to specifically pair with your amp. The double volume sounds like it’s a different label / terminology for a balance adjustment. Attenuation could mean several different things, could refer to gain as already referenced but without the ability to adjust attenuation or could be referencing the Pre’s ability to adjust the attenuation / gain. The ability to adjust the gain, attenuation if that’s what it references would be relevant when trying to match gain from various components. Shouldn’t be needed from your Pre to Amp if designed by the same manufacture and designed to pair together. As others have said, without understanding the lingo, tough to know what’s meant by some of the terms describing the various features. Attenuation could just mean one pre applies gain and the other is passive.
The more expensive unit could be targeting pairing their pre with other manufactures equipment, that’s where gain / attenuation matching becomes more critical.
Good Luck!