Would the twin engine Boeing Y3 be able to compete better than the Airbus A380?
The answer is quite simply, no, at least, not if it is or was intended to compete as an airliner of roughly the same size.

That's because your question is based on a false premise, that the struggles of the A380 in the current market are due to its fuel economy.

The A380 is indeed uneconomic to operate except on few routes, but that is because of its size and capacity - which on most routes, can't be filled.

The market has changed since the A380 was conceived and launched; airlines are using more and smaller aircraft with more connections, between more minor airports. 

To a lesser extent, new regulation has made a difference too. It has allowed smaller aircraft with twin engines - which are more flexible in an airline's operations - to take on routes that previously were considered suitable only for four-engined aeroplanes.

The technology and fuel consumption of the A380 are perfectly adequate to serve for decades into the future. It has been overtaken not by technological advances in its rivals, but by forces that change much faster than technology can: market conditions, and regulation.

Aircraft that will be selected instead of the A380 by airlines won't be chosen because they have better fuel economy (and even less so, marginally better fuel economy because they have two engines rather than four) but because they fit market needs better.