Advantages of 2-VSB vs BPSK?
Suppressing the lower sideband decreases the bandwidth by a factor of $2$ compared to BPSK. Since we're not talking about single-sideband (SSB) modulation, but vestigial sideband (VSB) modulation, we don't gain a factor of $2$, but a factor that is slightly smaller than two, because a part of one of the sidebands is retained.

Note that both BPSK and 2-VSB carry the information only in the (bi-polar) amplitude of the signal, i.e., only in the in-phase component, not in the quadrature component. The complex baseband signal for 2-VSB only occurs because the larger part of one of the sidebands is filtered out. This, however, is not necessarily done by complex baseband processing (using the Hilbert transform), but it can be done by applying a band pass filter after modulating the baseband signal. The latter option only uses real-valued processing.