Uhh...nope. I tried both decks and HHG just have a relatively higher chance than other decks to defeat Relinquished. It is still much inferior than this Relinquished deck. Running 3 Relinquished myself and it is the most consistent deck I have ever run, winning almost everytime when I could summon one by the 2nd turn.
@Edgar81539
You forgot to discard the second Thunder Dragon to get the third Thunder Dragon back and use switcheroo again on your next turn, in case you don't get all the cards you need.