Both BPSK and 2-VSB transmit one bit of information per smybol and both modulate the real part of the signal. The difference is, as far as I understand, that BPSK does not modulate the imaginary part of the complex signal at all, while 2-VSB uses hilbert transformation to suppress the lower sideband of the transmitted signal.

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.
• In fact, BPSK can use the imaginary part. For example, LTE uses a constellation rotated by $\pi/4$. Because as Peter said, the information is carried in the phase. – vaz Jun 29 '16 at 21:30