The question of balancing a plane Right-Side-Up, or Up-Side-Down is really a matter of the design of the plane.

Aside from Center of Gravity, you need to consider Center of Weight (CW).

In the first figure below, if you were needing to balance the Red bar, you would hold the ends of the blue bar with the red bar hanging below (as pictured). But if you were balancing the Blue bar, you would invert it and hold it by the Red bar, wouldn't you? That's due to the "Pendulum Effect" that N70R mentioned in post #2.

Now if you tried to balance the Top bar by holding the ends of the bottom bar, it would try to flip over to get the CW below the pivot point.

So depending on where the aircraft's Center of Weight is you might find it's easier to balance it either Right-Side-Up, or Up-Side-Down

A High-Wing plane will (Except in rare cases) always balance better Right-Side-Up, because whether you balance at the wingtips, or next to the Fuse, the CW is always below the wing.

But with a Low-Wing plane, the CW will always be above the wing at the Wing Root, but at the tips, it may be below, depending on several factors, including the amount of dihedral.

So the bottom line is, You can't just say one way is better than the other, but with a little common sense and maybe some "Trial and Error" it's not too difficult to figure out which way works best for whatever plane you are working with