Using the ARCH or GARCH tests depends on what your hypotheses are. I refer you to Box, et al., Time Series Analysis 5th edition, 2016, Section 10.2, ISBN 978-1-118-67502-1. This is something only you can determine, based on your data and what hypotheses you want to test. Also, you’re doing a meta-analysis, with different data sources, so the assumptions of these tests may not apply to your data.
I have the reference, so I scanned that section to see if I could offer some substantive guidance. (I can’t.) I’m not familiar with any of these, because they don’t normally apply to the sort of data I’ve worked with (that tend to be homoscedastic). (I also don’t have the Econometrics Toolbox, since I don’t do econometric analyses, so I have no experience with the functions.)
