I owned both DAC systems you are asking about, first the BADA DAC + USB, then the Lampi Big 7. The move to the Big 7 was a lovely upgrade for me and my system. It brought more of everything, and in a more holistic musical presentation. It was more informative about what is on the recording, and this seemed to bring greater harmonic realization, better timbre, a much more present and live feeling IME.
At first I fed my Big 7 from the Alpha USB to SPDIF and liked that. I only used that, because I presumed that it was simply a top notch input for a DAC, and I read that a lot DAC USB inputs weren't so good sounding. Well, I broke the Alpha USB converter input and had to send it in for service, which meant I was forced to feed the Amanero USB input that the Big 7 comes with from my Windows 7 PC directly. It was a very nice improvement in sound quality. Caught be by delighted surprise! I sold the Alpha USB and used the Amanero USB input until I sold the unit to go up to the GoldenGate. Yep, I got hooked on what a Lampi can bring to the music. Hope this helps!