I don't know what the risk of booking via Skylux would be in case of IRROPs, trip changes, or fare class booking (if mileage accrual is something of importance to you). So something to consider if worth the extra moolah. Personally, as much as SQ is a good airline, I probably wouldn't bother with it if I have to land in NRT. Both NH and JL are very good airlines in business class, so it's a function of price or alliance (for mile accrual).

So a number of variables: airline, airport, fare, booking agent. Airline: a tossup, in my opinion. Airport: HND is preferred. Fare: lowest is best, of course. Booking agent: would self-book, but depending on fare, and airport... I would try to narrow them down a bit further and rank them so you can make a decision. I fly Oneworld, so that automatically picks JL for me. So the only decision for me would the booking agent. I'd have to look into it further, never used Skylux. As a matter of fact, I've had enough trouble with 3rd party booking engines over the years that I've decided to book only directly with the airline, price be damned. But maybe Skylux is different?