Hello Nengi,
Welcome to the forums! :qiime2:
Both packages should work well for calculating alpha diversity values! Under the hood, Qiime2 uses scikit-bio diversity to calculate different alpha values, and Phyloseq uses Vegan.
Note that there are some differences in the implementation, like the base of the log used to calculate Shannon diversity. R / Vegan / Phyloseq uses natural log (base e) while Python / Scikit Bio / Qiime uses log2 (base 2).
As I write this, Phyloseq should not be used for calculating phylogenetic BETA diversity values, as there is an outstanding bug with how it calculates UniFrac distances.
But the alpha values are fine either way.