Well then :
- Newish plane : hard to say. First you can book because schedule said it is an A350 and then a substitution to an old B777 happens. But in general I would chose BA because you have a good chance to get a A380 I think.
- Lay flat seat : except if you choose Icelandair, I think everything will be lay flat on that route.
- Privacy : Lufthansa is not private at all. Other airlines have private seats on most fleet.
- Food/drink : all American Airlines are OK, BA can be good but is mostly OK, Lufthansa and Swiss too, Austrian is excellent, Air France very good too. SK is bad.