I've been to both cities multiple times and recommend you consider visiting both over the 10 days. It's about a 6-7 hour flight between the two. Both have excellent shopping, restaurants/food options, excellent hotels, sightseeing, etc. I think 10 days in one would be a little long. You could split the 10 days between both.
Another recommendation if you wanted to stay in only one city for the 10 days is to take side trips to see other sites. E.g. Go to Malaysia from Singapore or take a bullet train to Kyoto or Mt. Fuji from Tokyo.
Good luck with your planning!