Sounds like you could use either hinge. If you're going to go with the piano hinge, you need to cut the wood that the hinge attaches to a bit shorter than the other pieces. If you do this correctly, everything should line up.
If your box is already put together, you may have trouble getting either type of hinge to work. With a Euro hinge, I think you typically need a little gap between the "door" and the side the hinge is attached to. The hinge allows you to adjust the gap, but if you make it too small, the door may not have enough room to open. A "zero protrusion" hinge might work around this problem, but I don't know for sure.