Hi Jaff,
The chief advantage of a longer arm is that the overall tracking angle difference, from outer to inner tracks, is reduced, because the radius produces a circle segment that is "flatter" than with a 9" arm. You therefore get a truer contact of the stylus with the groove walls, throughout the side.
I found this illustration - ideally you want the stylus to follow the straight track from the PU-head to the center of the record, but the arm will draw a circle segment that never really coincides with the sound carrying portions of that straight track. the longer the tonearm, the flatter the segment however, corresponding closer to the straight track.

Of course, B&O later solved it elegantly by developing the tangential tonearms, that follow a straight track, because the base of the arm moves relative to the stylus position, thus securing perfect contact between the stylus and the two groove walls.
Potential problems with a longer arm is the introduction of resonances, but that is damped through various techniques.
My 9"-tonearm is excellent for opera, I really like how voices come across with it - this may, of course, also be due to its SP 8/9 PU; the 12"-tonearm gives a very wide and airy soundstage, wider than the 9" - but is more prone to transmit surface noise from vinyl that isn't quiet - this may be due to the longer arm. However, it delivers amazing punch to percussion, and I have a blast playing a variety of music with it. The 12"-arm is also more sensitive to small changes in tracking weight, and I feel I can almost "tune" the music by adjusting the weight, with it. I have a digital scale which I can use, but it's fun how well it corresponds to the numbers on the vintage tonearms.
A longer tonearm plays truer, and creates less inner-groove distortion.
I'm going to mount a Schick tonearm with an Ortofon SPU pick-up on the deck, on a shouldered tonearm board - the vintage PUs I have now have trouble resolving past 13.5kHz, on some records cramping high-hats, cymbals - so I'll have to get something non-vintage, as an alternative, while retaining the elegance.
I think the Schick arm will look stunning on the Beogram 3000 Thorens. This is also a 12"-tonearm.

I should mention that I now have the Beogram 3000 very nicely set up, the mechanism is completely silent - I spent some time silencing it, after getting it home. Something that one should expect to have to do, in spite of it being newly refurbished. Just working with the set-up, the perfect leveling, lubrication, the belt. For instance, I had the power cord in contact with the motor casing, and that transmitted noise that was picked up by the stylus. Little tweaks and adjustments that in the end resulted in a completely silent Beogram - I can now place the stylus on the chassis, and only pick up the faintest hum from the motor, even at loud amplification - which has me wondering whether I really want to move the chassis to a slate plinth. I like to keep it "original".
