I would be surprised if they beat PSG. I know that they have been good and they tried to make it to the quarter-finals, but I don't see them making it to the semis. I rate Emery a lot and I believe he's a top manager, if anyone can do it then it's him but in this case, the quality of PSG is way more than that of Aston Villa. Also, Enrique is not a small coach, he's a good tactician too.
If the match was a single match then Aston Villa will have a better chance because they can defend well and score a goal and qualify but a two-legged tie makes things very difficult for them to qualify. PSG will make it to the semi-finals, but I don't know if they can win Madrid if Madrid qualifies.
We need to give Villa their flowers for coming this far in the competition. I didn't expect it, as they even made the top 8 in the group stage earlier. But just like you and others have said, this might likely be the end of their journey in the competition. With the way psg played against Liverpool, I don't really think Villa can absorb that same pressure. psg's attack has what it takes to crack villa's defense, so the game is already a win for PSG (both legs imo).
I won't be surprised to see PSG and Real Madrid in the next round. They are the favorites, but anything can happen in football. Liverpool was also the favorite to even winning the title at some point, until the unexpected happened.