Tokyo, overall, is much more compact and dense than London. This surprised me quite a bit; I had visions of cobblestoned narrow streets. I finally got to see some of them around the British Museum and Covent Garden, but they don't seem "the norm" these days; two lanes of traffic with two lanes of parking is much much more common. The stores, apartments, and houses are similarly bigger in London; the only place I've consistently had to duck my head is getting onto some of the Tube lines.
Tying into the "compactness" thing - public transportation is generally much better in Tokyo. The trains (and buses) run on time, don't break down at the drop of a hat, aren't closed at random times, and have an actual schedule. On the other hand, the bus networks in London seem like they're better (if slooooow) in terms of coverage. They're also much cheaper than the subway, the opposite of Tokyo - but Tokyo is the only place I've seen where the trains are cheaper than the bus.
Food: Tokyo wins, hands down. Tasty food is ubiquitous, and quite frankly difficult to avoid. London, on the other hand... well, I've been told that tasty food does exist in many places, I've yet to encounter much of it. You'll pay out the nose for it. And speaking of...
Cost of living: I thought Tokyo was expensive. Hoo boy, not compared to London. Tokyo prices seemed like they were about 20%-50% than equivalent US prives for most things; London prices AFAICT are about the same as if things were in dollars, which is about 50%-60% higher. My one bedroom apartment is £280 a week, or about $1900 a month. I suppose it would be about the same as Tokyo, square meter for square meter, but it's still a big outlay. Hotels are much more expensive than in Tokyo - unless I don't know where to look, which is an eminent possibility.
Boozing: I'd say that when dealing solely with alcohol, the two are about tied. London's beer is really quite nice, isn't too expensive (around £3 for 500mL, usually) and the pub atmosphere seems fairly convival. The pub grub doesn't compare to izakaya food, but that shouldn't be a surprise with Japan's gourmand culture and England's lack thereof.
Culture (nightlife): ...this is a toughy, since I haven't been exposed to much of it yet. It looks like many events (live music, clubs, etc) will be much easier to find here, but that could be due to my 日本語 being terrible. Time Out does list all sorts of things in one convenient place, however, and I didn't see anything comparable to it in Tokyo. I haven't yet made it to any club nights, or concerts, or warehouse parties or whatnot, so the jury is still out.
Culture (artistic): Another "jury is still out", but I'm leaning towards Tokyo having a larger (if less participatory) venue and corpus. In Tokyo, it was difficult to walk down the street without seeing somebody reading manga, or a hand-chalked sign hawking some sort of wares with happy little animals decorating such. While I know there's lots of art around here, I suspect it's more relegated to museums and galleries and whatnot - that is, art is by Artists, not by anyone and everyone if they feel like doing so. I'd say that the former is probably a general Western thing - although with things like the Make fairs and Burning Man, they might be getting better.
Possibly to come in future installments: comparisons of bureaucracy, people, day-to-day life, jobs, cultural attitudes.