As somebody who did exactly what you have done about 18 months ago I would say "It depends".

I have stayed with BA and then also joined Velocity (Virgin Australia's programme). My reasoning is thus:

1) Our company policy is Premium Economy rather than business and I fly to SIN a lot. QF don't have a well timed PE offering to SIN so it's either SQ (who's PE isn't great) or BA. Already having status with BA makes PE pretty good especially for a day flight and I usually use Avios to upgrade any overnights. QF have a great PE offering and I use it for HKG when I fly there.

2) If you use Corporate Traveller (part of FlightCentre) as your travel agent for at least one booking then they have (?had) a great offer which got you trial Velocity Gold with an easy to complete challenge. Retaining Gold (and soon to be platinum) has been easy doing my domestic travel on VA and the occasional hop to NZ / SIN on a partner. VA status gets you benefits on NZ, SQ, SilkAir, Virgin Atlantic and a couple of others I think so whilst not *A it covers this part of the world quite well.

3) I was Gold and retaining that with BA is actually not too difficult if you pop back to the old country a couple of times a year and if you split your flight at SIN (i.e. the BA16 followed by the BA12 / BA11 followed by BA15) then you can do your four segments in one return trip.