SQ Suites on the A380 are excellent if you're travelling as a couple, book 1A 2A or 1F 2F. You may want to check seat maps on ExpertFlyer or an equivalent site before you book a given flight, as the size of the suites gets smaller each row back (ie row 1 is bigger than row 2 which is bigger than row 3), so even for solo travellers people tend to book rows 1 and 2 first, making the double suite unavailable.
One thing to consider for daytime flights is that the seats for meals are on the opposite sides of the bed in the double suite, so it's actually harder to sit together to dine if you want to do so. When my wife and I have flown in Suites the crew usually offer to setup a small stool in one of the two suites so we can sit on opposite sides of the dining table. If you like the idea of eating together on a plane, QF First is the best option as they have a fully belted jump seat on the opposite side of the table.
The SQ 777 is also a good option for daytime flights, if you are happy to pick the middle seats and give up a window view. It's relatively easier to have occasional conversations while each staying in your own seat, and there's a lot to be said for the ratio of 4 pax, 2 crew, 2 toilets and what seems to be the same load of champagne as for the 6 Suites on the A380.
As others have mentioned, the Private Room in SIN is probably the best lounge experience you'll get between Australia / Singapore / Japan, it really is exclusive and the food and beverage is top notch. The QF First lounge in my opinion does better food than the small SQ First lounge in SYD, although the SQ lounge is much much more private and quiet compared to QF which can get absolutely crowded.
JL First on the 777 is probably more suited to solo travellers, with the higher walls and no space for someone to dine with you. The food and drink is always exceptional, but you're in the same QF lounge out of SYD and the JAL First lounge in HND is more like the QF one than the SQ Private Room.
If it were me and I wanted to maximise my enjoyment on a one-off special trip I'd book SQ. Try the 777 on the daytime flight to Singapore for the most exclusive cabin, easier casual conversation with your travel partner, and if you're lucky not to have any other pax in F on that flight the closest most people will ever get to a long-haul private jet experience in the air. Book the A380 Suites in rows 1 & 2 on the way home to take advantage of the double bed for the overnight flight which again you won't find anywhere else short of Etihad's Residence or a private jet.