Here's the way I see this card:
It's GREAT if your opponent is running a stall deck or a deck with cheap cards. And *eventually* you'll be able to play the same deck your opponent plays, kinda. Sometimes times ten.
However, you DON'T get the cards of your opponent's hand, and it will take a turn or two to get one out. And getting one out doesn't mean you win, not even two, since the opponent had that great card advantage at the start and you're using your deck for aether quanta and mind gates (essentially taking up slots of your deck). And in many cases, there are cards that are completely useless to draw, like dragons before you get pillars, animate weapons especially, and such. Keep in mind you can only have 8 cards in your hand, so it's not like you CAN play their deck x6 unless they get the perfect sequence of draws for you. Once you get 4 mindgates out, unless their next card is a pillar, you probably will only be able to use it 1 per turn, since not only do you have the cards of THEIR deck in hand, but also the cards of YOUR deck.
And if the opponent gets their only weapon or something on the draw, then you'll never get it.
AKA, effect is strong, but very dependent on your opponent's deck and the sequence of their draws. But not so strong that it should be 6 aether to play and 3 aether for ability. That would make it unplayable. Some decks are liable to be owned by this, namely decks using shards.
Wait wut? AMG! A card that counters shards! I thought that's what everyone wanted?
And that's all assuming your opponent has no permanent control and such. That's assuming you'll always be able to play and use it aka, no denial whatsoever, which is rather rare.
All that said, I say the 1 aether casting cost may be a little too cheap. Instead, make upped version 3 aether to play and 2 aether to use the effect.