The shape and distribution of mass of the object can also have a big impact on how you lift it.
An automobile, for example, is much heavier on the engine side than the other side and teh centre of gravity can be quite high.
If you tried to lift it straight up in the orientation it would be if standing on land then you would (a) find that very difficult to control and (b) once the object broke the surface the centre of gravity would be too high and it won't behave. IN the case of a car, for example, it would probably flip over upside down once you got it to the surface even *if* you managed to get it to the surface in the orientation you thought you wanted.
Staying with the car example, What TC says is true too. Assuming the car was standing upright on the bottom and it's whole bottom was in contact with the mud then suction becomes a big issue. Think of the bottom of the object as a big suction cup. If you were to try liftin it with one big baloon on each wheel then that would be like trying to pull the suction cup straight off of whatever it was stuck on. But if you tried to lift a car by only one back wheel (assuming you found a point to attach that could take the weight) then it would be like pulling the edge of the suction cup away, which would make the whole object come loose from teh bottom easier. Also in this example, lifting it from one back wheel would leave all of the mass under the balloon so no part of teh car would break the surface and it couldn't move strangely once you got it there. IN other words, the lift would be easier to initiate and more controlled. (incidentally, if you don't want to experiment with a car, you can use an old bicycle and just tie a 20kg weight onto the front forks).
All this is to say that where you attach the balloon(s) has to be consciously and carefully chosen and that poor choices can lead to problems.
So bringing this back to the OP. The first couple of posts are correct that the orientation of an object under water won't affect the total amount of water it displaces but the shape, surface area and mass distribution are critical factors to consider for *how* you approach the lift.
R..