to really answer your question, I need to know a few things:
Where does it say a TIE has the exact same firepower as a TIE advanced?
Which frigate are you referring to?
What type of shield generator did that frigate have?
What type of shield generator did the rebel command ship have?
*Please answer the above questions footnoted with canon references please. If you do so, we might be able to sort this out.
You don't need any of that. Who is going to make a capital ship with weak shields that a fighter, with laser cannons, could take down? You wouldn't. That's why the fighters have torpedoes. They aren't carried to take out Death Stars. Now you could make a claim that *maybe* Vader somehow was inside the shields, if that's possible. Otherwise it doesn't make sense.