Good choice between the two.
As you mentioned one night less in a hotel, plus better hours at the airport with the lounge.
Hopefully you'll also catch some zzz's on the plane and breakfast will of course be served in the morning.
Haneda has a lot of interesting food options before you clear passport control. Lots of choices, really. Once you go airside there's just the lounge that will be of interest.
In Tokyo you might want to stay somewhere like the Shiba Park Hotel or someplace similar within walking distance of the Hamamatsucho Station, from where the monorail to Haneda departs. Every so often there is an express train that takes you straight from this station to the Haneda International Terminal. No stops along the way.