In short: Yes, you can use the $BIC$ (and $AIC$) information criteria, assuming the following:
All models are applied on exactly the same data set.
All model parameters are estimated via maximum likelihood estimation.
Your sample size is much bigger, than the amount of parameters in the models (as GARCH models don't have many parameters, this will probably be no issue)
Even though it is often claimed, the compared models don't need to be nested for the $AIC$ and $BIC$ to be valid.
Lastly, note that there is no "best" way in model selection. It all depends on the purpose of the model that you are looking for - usually, in a real life setting, the true model isn't even one of the candidates. However, $AIC$ and $BIC$ can usually give you a good idea, which of the models is preferable.