It’s a no brainer to go for JAL F rather than BA F in my opinion if you have the option.

One of the two BA flights goes to Narita, the other to Haneda. Currently the 789 only goes to Narita and is quite a way from downtown Tokyo when compared to Haneda.

I much prefer the timing of the outbound JL44 (their other flight doesn’t have F), where you have time to enjoy a decent evening meal, have a reasonable shuteye, and be in your downtown hotel easily by 4pm, giving you time to do some shopping (my penchant as an accomplished nerd is to head direct to Akihabara, but YMMV).

I had the multi course Japanese menu a couple of weeks ago LHR-HND, it was as good as it gets. The Western menu on the return was pretty good too, I chose the Wagyu fillet. And there’s caviar too of course.

FWIW, the Champagne is currently Cristal 2009 and Bolly Grande Annee 2007. Here were four whites on my flights, including a Montrachet 1er Cru 2015, NZ Sauv Blanc, Italian Pinot Grigio, and a Japanese orange wine which I loved. On the reds, there were four, with a Branaire Ducru 2014, then three pinot noirs, one from Burgundy, one Californian and the other from NZ. There were also two sakes and two shochu. Also of note was a premium tea, “Queen of the Blue” from Royal Blue Tea which apparently is a thing, it tasted fine, it’s served cold out of a wine bottle, no milk of course!

Regarding lounges, at LHR you have the large selection at T3, I had a shower in the Qantas lounge and then a couple of cocktails propping up the bar upstairs, but ended up at the Cathay biz lounge propping up their bar instead as the bartenders there seem to be able to operate without needing a cheat sheet, and it was difficult to get any attention at all at times in the QF lounge despite sitting right at the bar itself.

The F lounge at Haneda is pleasant enough, but I wouldn’t care to spend too long in there. FWIW, the F lounge at Narita is in the same league. I found the food options somewhat lacking, ANA’s F lounge is a little better in that respect.