I personally have been trained in both methods.
Now, I'm an advocate of "do-what's-right-so-long-as-it-does-not-impede-your-playing-in-any-way" school.

To me, both schools have their merits, and tend to make certain aspects of life easier while making another aspect harder.
Also, I wonder if it's only me, but repertoire often dictates what part of my body that I'm going to use more.
For example, Baroque~Classical~very early Romantic era stuff requires very precise finger work and articulation. On the other hand, as you progress further into the Romantic era and ultimately move into 20th Century stuff, it ain't just about the finger work anymore; there are more moments where getting the arms and wrists more involved is definitely a necessity.
One cannot aim to rely solely on precise fingerwork to play wide, sweeping intervals of the more "modern" (i.e. more modern than early Romantic) stuff;
likewise, one cannot aim to just "arm" everything and hope for the best on the tight, sixteen notes of ye olde days of Baroque and Classical era stuff.
As mentioned by one of the replies, the finger and hand are forever married to the wrist, arm, and the torso, and only by working in harmony can one aim to achieve the optimum results.
With this being said, the "bias" seems to lie more or less on different body parts depending on what you are required to play.
Again, trying to play wide, sweepng intervals with fingers alone? Good luck.
Trying to achieve articulation with "arm alone"? Good luck.
In your opinion, what aspects of playing does the "finger school" make easier?
What aspects of playing does the "finger school" make harder?
How about the same questions for the "arm school"?
What is your preferred way when you play the piano?