I don't know why exactly you picked those dates, but they do make for interesting ones! Being in Kyoto in 1447 would mean living in the middle of the Muromachi period, of which the Ashikaga Shogunate was the central fixture. Although officially the Emperor (Tennō) was still the head of state, actual power was concentrated in the Shogun, military leader of Japan. The Muromachi period is the only period in Japanese history where both the Emperor and Shogun resided in the same city, Kyoto.

As the political heart of the Empire, the city was filled with the mansions and palaces of nobles. These nobles could be roughly divided into two groups: the court nobles who held their titles due to their lineage (often related to that of the Emperor) and the warrior class who controlled the Bakufu after the failed Kenmei Restoration 100 years prior. Historically the location of a nobles' mansion partly determined their stature within the state, with locations closer to the Imperial palace being reserved for higher 'rank' nobles. The Muromachi Period however added the interesting dynamic of also having the Shogun establish his residence in the city (in the Muromachi area of the city, hence the name of the period) and as such the dynamic of where exactly you lived in the city had an extra layer of complexity. I should note that historically the city had a completely geometrical shape, familiar to many US cities. The city had a population of around 150,000, making it the largest city in Japan and one of the larger cities in the world (about the same size as Paris). The vast majority of people in the city would however never even see one of the higher nobles due to the rigor of the hierarchy system.

The Muromachi period saw an increasing amount of interest in Japan's native Shinto religion, which previously had been relegated to a secondary position (at court at least) in favour of Buddhism. As such, in 1447 you would likely have been able to see the consecration of many new shrines, but also the construction of new Buddhist temples on the outskirts of the city, such as the Ryōan-ji, completed in 1450. Overall the city would appear peaceful and prosperous, with monumental palaces and mansions abounding. That said, Japan was very much feudal at this point and travel was limited mostly to merchants. Along with the hierarchical structure of society, the vast majority of people would never be able to look at these wonderful structures.

However, this peaceful exterior hid the rising tensions facing the Ashikaga Shogun. The palaces of the nobles were maintained largely through tithes granted by the Emperor or Shogun. These tithes would however be administered by the nobles personally. In practise what happened was that nobles would appoint someone to oversee their holdings in the countryside as leaving the court would damage their position. Ever since the Heian period a few hundred years prior, the power of these local administrators had been growing. Many of these administrators would eventually form the backbone of the 'Daimyo' feudal nobility. Either way, the power of the Shogun was ebbing, with more leverage going to the countryside. As such, when an imperial succession crisis broke out in 1467, the Shogun no longer had the means to control the situation. Over the course of the Onin War (1467-1477), the Shogun lost control over the country, precipitating the Warring States period. Kyoto suffered heavily, and many of the buildings and palaces one would see on a visit in 1447 would have been torched. Half of Kyoto was sacked and burned during this time. If I were to try and make a modern parallel, walking through Kyoto in 1447 would be akin to walking through Warsaw during the Interbellum. Many of its famous structures were looted and destroyed, and the city never recovered its unparalleled stature in Japan.

I find the parallel between 1447 and 1847 rather interesting. Both dates are just 2 decades prior to society-changing events. 1447 due to the Onin War and 1847 due to the Meiji restoration.

Kyoto in 1847 had recovered from the disastrous events it had witnessed 300-400 years prior, but had faced more recent hardship. A series of failed harvests in the latter half of the 18th century saw the urban population of the city drop dramatically. By 1847 Kyoto had not quite recovered its size, but still had a very respectable population of around 300,000. It had however been eclipsed both demographically and economically by both Edo (later Tokyo) and Osaka. Following the Warring States period, a new Shogunate was established (Tokugawa), which established itself in Edo, meaning the political center of the country also moved. As such, apart from being the residence of the Emperor, the city wasn't of the same national importance that it had previously.

The city was however largely shielded from outside influence and continued to be the traditional cultural centre of Japan. As such, the city became somewhat of a tourist destination for the new economic middle class of Japan, constituting merchants and samurai. Although pleasure travel had been largely limited or banned by the bakufu, many found excuses to travel by way of obtaining pilgrimage permits for the many temples located around Kyoto.

For those not able to obtain such permits, or did not have the financial means, the mass production of woodblock prints of Kyoto's many views became a novel way of enjoying Kyoto's heritage. Kyoto was the first place in Japan of which (private) tourist guides were published. These guides, by the 19th century often illustrated, not only highlighted the different temples available to visit but also noted artisans worthy of visit, and sometimes even rated the brothels and Geishas, of which the latter Kyoto had become particularly well known for. The city's clothes were also particularly prized, with Muromachi street becoming more known for its kimono vendors than the long gone Shogunate residence.

Architecturally the Kyoto of 1847 was not that different from 1447, apart from few missing landmarks. Houses were in both periods constructed mostly from wood, of which the layout was not particularly different. Perhaps more interesting to the tourist is that at least in 1847, you could view a lot more of the city and its landmarks than in the heavily feudal Muromachi society.

1847 is just two decades prior to the Meiji Reformation, heralding unprecedented change for the country. Even in the 1840's, the Tokugawa bakufu had become much more unstable than ever before. However, unlike during the Muromachi period, Kyoto was mostly spared the warfare that prevailed during this time, perhaps partly due to it being the Emperor's residence, to which both the existing and revolutionary orders pledged loyalty.

The major difference between visiting in 1447 and 1847 would be the ability to actually move relatively freely around the city and be a tourist. Expert artisans, priests and prostitutes were present in both periods, but in 1447 these people would be peddling their livelihoods more towards the denizens of the city. Although obviously still the case 400 years later, the advent of modern tourism and export had given the citizens of Kyoto a much wider, national, appeal.

There's much more to be said on the topic, but I hope this gives at least a little insight into the question!