FRB Cleveland's working paper website just post this paper by Todd Clark and Francesco Ravazzolo "The Macroeconomic Forecasting Performance of Autoregressive Models with Alternative Specifications of Time-Varying Volatility"
It compares AR models with various time-varying volatility specification including
stochastic volatility (both with constant and time-varying autoregressive coefficients),
stochastic volatility following a stationary AR process,
stochastic volatility coupled with fat tails,
GARCH,
and mixture-of-innovation models.
Is the replication available here especially that he used to post VAR-SV model here