comparing ScRNA-seq data from two different studies: should batch effects be corrected with pooled cells or not?

Question

[demoraesdiogo2017]

Hello I would like to compare T cells from this study https://www.medrxiv.org/content/10.1101/2020.04.17.20069930v1.full.pdf with T cells from this study https://www.nature.com/articles/s41591-020-0901-9#Sec2

However, I'm not sure if I should remove batch effects from each dataset separately or with both studies pooled, especially because each author used a different method.

Perhaps selecting the cells I want and performing a differential expression analysis would be better?