Is it a normal fare they are using - as in, any sort of J fare (nett or published) as opposed to the current specials in J SQ were/are offering? Only mentioning it because if it's the specials (75%-50%) they apparently don't accrue miles.
Other than that, both Aeroplan and Mileage Plus are always good bets for easy status, accrual rules and for the most part redemptions. SIN-ICN you will be able to have a choice of SQ OZ TG and NH for the one trip with transits in BKK or TYO if you use TG or NH. If you join MP, then there would be a cheaper reward using UA metal only SIN-NRT-SEL, although I'm not sure if MP rules will allow the direct transit at NRT.
Like any decision on which FF scheme to join, your choice should be influenced by what part of the FF is important to you, (miles for rewards, or status or both) and your travel habits and regions of travel.
Cheers.