Main Reinforcement Direction

There will be a greater area in the long direction because the moment will be greater.

Most likely the long direction. However, it depends on the relationship (geometry) between the footing and the column pier, transecting walls, or directly bearing column baseplate.

Each case must be assessed and analyzed on a case-to-case basis.

Don't forget that reinforcement is usually required in regards to both axis, as there are applied bending moments (and shear) present in each direction.

And don't forget to check and design for one-way shear, 2-way shear, and punching shear!

I forget to include a very important factor in reinforcement of footings (and other concrete structural element)....

According to ACI 318 standard, minimum reinforcement ratio (Rho) for ASTM A615, Gr. 60 steel is 0.0033. Therefore, you'll need to reinforce the concrete element in both axis no matter what, unless you can demonstrate by analysis that the design tensile stresses doe not exceed the allowable tensile stress.