Whether it is a cheap restaurant or a fine and famous place, sushi in Tokyo will be better than in Europe most of the times. At least the fish will be fresher and more various. How the fish is cut is another issue. I don’t think that thick pieces of fish are typical only to cheap places, I heard that famous chefs do that too, but I hate when the slices of fish are so thick, you feel as if you a chewing a whole fish in your mouth!
This is what happened to me in Edogin Honten, a casual sushi restaurant close to Tsukiji market.
The thick slices of toro were ok as toro usually has quite soft buttery texture and you can actually bite a piece of sushi…
.. but what bothered me a lot was the size of yellow fish as it was big enough to make two sushis!