I'm going to make a tentative 2nd post on the sub, Firstly I'll point out that medieval era is generally only a term applied to Europe and it ended in the 15th century about 150 years earlier than when Shogun is set (1600). However, easy mistake to make and the rest of the question is valid so I'll go with 1600s.

There are a few reasons that I know of: One, large cities were relatively new in medieval Europe (the massive population decline following the collapse of the Roman Empire and the dark ages had seen most of the large ones either collapse or diminish greatly), they hadn't yet redeveloped sewage systems since emerging from the dark ages, and as such they didn't have effective systems for 'waste' disposal.

Two, Japanese society used human waste as fertilizer fairly commonly, and as such there was a financial incentive to the removal of waste from cities to be used in farmland, in other words it was an occupation (though admittedly not prestigious or popular)

Three, Japanese cities were larger in terms of population, than was generally the case in Europe. At the time Tokyo had a population of 300,000+ which was more than either London or Paris which meant there was a larger urban workforce and thus larger specialised workforce.

Four, People in Japan were generally speaking cleaner at that time, thanks in part to the climate and the prevalence of hot springs many people were able to wash without having to heat water which was expensive for the average person.

Five, Cities in Europe were complicated affairs, often run under town charters giving certain freedoms and for the most part they were separate from the feudal structure meaning that citizens of cities were generally not considered peasants or serfs and as such were not indentured labour. This was not the case in Japan where cities were owned and run by Daimyos who often lived inside of them (While both Europe and Japan were agrarian based the consistency of urban dwelling in Japan meant that the daimyo were highly integrated into these economic and population hubs whereas European Feudal lords were still living in their ancestral castles in their main economic base, rural farming communities), as such it was prestigious for them to have clean cities. Whereas in Europe cleanliness of a city was not the responsibility of anyone in particular and as such it generally didn't happen.

Unfortunately it's 2am in Australia and I cannot find my sources, if you're interested in the European side of cities I recommend http://www.fordham.edu/Halsall/sbook1.asp which has many great primary sources including some town charters. Hopefully this isn't deleted and it helps!

edit: oh and as for Osaka specifically, apparently bigger than London at the time too, Tertius Chandler, "Four Thousand Years of Urban Growth: An Historical Census", The Edwin Mellen Press, Lewiston (1987).

I am not a historian of early modern Japan, as you can probably surmise from my flair, but I thought I'd throw this out there as it recently came up in a conversation I had with a friend. Everyday Things in Premodern Japan: the Hidden Legacy of Material Culture is an absolutely fascinating book. I read it for an undergraduate "Japanese Civilization" class and it answers this question perfectly. https://www.worldcat.org/title/everyday-things-in-premodern-japan-the-hidden-legacy-of-material-culture/oclc/42922572&referer=brief_results. I wouldn't be surprised if someone answered this question, but if you want a whole book on the subject, check it out.

Another interesting and possible reason for Japanese cities being thought of as cleaner than European cities might lie in religious reasons.

Shinto is heavily centered around cleanliness and purity. Cleanliness of holy places, shrines, the home, communal areas, and of course, the body.

For example, before one was allowed onto the premises of a shrine, they had to cleanse their mouths, hands and feet. Even today you're supposed to ritually cleanse yourself by washing your hands and mouth at a small fountain at the entrance to shrines.

Religious figures, like priestesses and priests were even more stringent and set a standard of cleanliness.

Uncleanliness was directly associated and often even referred to as being the exact same as impurity of the spirit, or in other words, being dirty was equated directly with sinfulness.

Also, respect of one's environment and communing with nature is one of the spiritual pillars of Shinto. The idea that god(s) were a part of and in everything cultivated a massive culture of respecting all things, including the inanimate.

Mountains, rivers, and forests were seen as holy, spiritual and deserving of respect, care and love. This extended to the very earth they walked on, the homes they lived in, and the tools they worked with.

There was and is an internal spiritual mechanism built into Shinto that leads followers to be more inclined to not pollute or dirty their cities.

This is in addition to all the other very substantial reasons that /u/lkentfahey already mentioned.