Since the OP usually flies VS, I don't think he's really interested in obtaining status on *A, but more concerned about crediting the redeemable miles where they will be useful (OP, please correct me if I'm wrong). You don't state where you are located, which potentially has an effect on what choices make sense, but I'll assume you are US based.

The trip should be 7268 miles each way, I'm assuming a round-trip of 14,536 miles in business.


Asiana Club
Depending on the fare class your ticket is booked in, you receive 100%-135%, so 14,536-19,624 Asiana Club miles. Asiana has a zone-based award chart, and allows one-way travel for half the mileage (on Asiana), so this is enough for some short-haul travel on Asiana.

United
Depending on the fare class your ticket is booked in, you receive 100%-135%, so 14,536-19,624 MileagePlus miles. This is enough for a one-way domestic saver award on United.


In light of this, I'd consider crediting to a program with a mileage based award chart like:

ANA
Most business class tickets on OZ accrue 125% on NH, so 18170 Mileage Club miles would be credited. ANA has a distance-based award chart, so this is enough for most domestic round-trips (on ANA, depending on season), or international travel of up to 4,000 miles (total, on ANA, depending on season).

Another good question is do you plan on any travel that can't be credited to VS, that might be combined with this trip's mileage? Also, depending on your travel patterns, planning to use this mileage for an upgrade rather than an outright award ticket may make more sense.

Asiana also partners with some non-*A carriers, like EY and QR.