I have a pair of Conquests and I can say if they are mated with the right speakers (AN-E's) you will likely not find a more satisfying combination. The SS version has silver wound output transformers, all blacks gates on the 300B board and power board. The 300B is an amazing sounding tube, designed for audio. The 6C33 triode used in the BAT was certainly not. The downside to the Conquest is it is only 17 watts. Now if you use an efficient pair of speakers, as they were designed for, you would never need more power than that.
The BAT is a hybrid push pull type, making 120 wpc per monoblock. Your speaker choices will be almost unlimited. But these amps were NOT designed for the high efficiency alnico or horn type speakers that the 300B Conquest was designed for.
In short, the Audio Note was made for someone going in the direction of a low power SET system. The BAT certainly is not designed for someone moving in the low power SET direction. So they really are designed for two separate and divergent segments of audiophile nervosa.
If you are not looking to spend some major bucks on associated gear with silver transformers, silver wire, and speakers with silver voice coils and alnico magnets, then I would avoid the Conquest SS amps. Those are for low power SET purists, building a system with as much silver as possible in the signal path. Not to mention the Conquests cost about 16k for the pair, and the BATS can be had for much much less than this.
If you are a budding SET purist, then go for the Audio Note stuff by all means. There is nothing else out there that sounds like it. It is like heaven I assure you, but you have to be committed to building the system correctly to get the most out of them.