Hi @Eudemon,
Welcome to the Affinity Forums
Thanks for your files provided! I can confirm there a few things happening here.
Firstly, without the correct fonts installed then it's very likely that these will not match, as the replacement font in use will not visually match the original font, therefore the fx will be applied to the replacement and may not match.
Secondly, unfortunately Affinity Photo doesn't currently support all the same layer fx that Photoshop does - so certain features or styles may not match exactly.
However, if you want these to be a much closer match and don't need to edit the text itself, then under Edit > Preferences > General you can untick Import PSD text as text rather than bitmap & reopen this file.
This should provide a more accurate representation of the file, at the cost of text editability.
I hope this clears things up!
