|Quoting a380900 (Reply 2):|
No difference between A340-500 and A340-600. Maybe one between A340-200 and A340-300.
The A342, 343, and 333 have the same (short) fin, while the 332, 345, and 346 got the tall one. Even though the 345 and 346 have a longer moment arm, the Trents are far more powerful than the hair dryers on the 342/343. Boeing had to change the rudder on the 748 to a double-hinge to regain authority, despite the fact that they stretched the aft fuselage (1.6m IIRC). My guess is that the 744 was at the absolute limit with its 62k engines and a rudder designed for 43k JT9Ds from the 741, so the 67k GEnX on the 748 necessitated the change.
With the 389, I suspect they'll keep the same fin as the 388, because the moment arm and extra engine thrust will cancel more or less. My guess is that the Airbus guys did their homework and future-proofed the fin for use with the 389 the same way they overbuild the 388 wings for a larger MTOW. That way, if they do go with the stretch, they can keep the production process the same without having to twiddle with anything.