What are the pros and cons of using multivariate Filtered Historical Simulation with univariate GARCH models compared to a GARCH-DCC approach?

I am assessing the market risk of an equity portfolio and have come across an example in the MATLAB documentation that uses a multivariate Filtered Historical Simulation technique:

https://it.mathworks.com/help/econ/using-bootstrapping-and-filtered-historical-simulation-to-evaluate-market-risk.html

This approach combines univariate GARCH models with a nonparametric specification of the probability distribution of asset returns. FHS allows for the generation of forecasts by bootstrapping standardized residuals and simulating future returns.

I am also aware of the GARCH-DCC (Dynamic Conditional Correlation) approach, which models time-varying correlations between asset returns. I am interested in understanding the pros and cons of using FHS with GARCH models versus a GARCH-DCC approach.

Which are the advantages and limitations of each method?