Here are a few things which separate the way a peasant might haved lived during the Heian (1050 AD) and Tokugawa periods (~1850 AD):
Housing
Believe it or not, the oldest house in Japan that can be dated is from 1607 AD. Housing changed dramatically between the two periods you are referencing, both for the the "nobility" such as daimyo and peasants as your question concerns. These advancements in housings led to the more permanent structures which are still able to be studied today.
In general, poor families saw an increase in wealth from the 15th and 16th centuries onward and that led to an increase in the quality of housing. As this trend diffused throughout Japan in the 17th century, commoner's homes began to be increasingly wood-floored (as opposed to their earthen predecessors). Plaster began to be used more ubiquitously on walls. Houses also began to be constructed more symmetrically, for example using right angle corners placed upon foundation stones.
Overall the improvement in housing led to not necessarily a higher quality of life, but certainly a higher quality of home with better insulation that would in turn be sturdier and more weather resistant.
So in comparison to the Heian period, housing became sturdier, more symmetrical and more complex for peasants.
Religion
Around your timestamp of the Heian period, Buddhism did not generally reach to the peasantry of Japan. Attaining salvation under Heian era Buddhism was largely an aristocrat's game - to do so meant to give expensive donations/favors to monasteries. This resulted in monasteries concentrating more on attaining power and connections to the aristocracy than reaching out to the masses. There were still Buddhist priests concerned with reaching out to the peasants, however, such as the monk Kuya (~930 AD) who travelled the land construction bridges etc. and spreading the word of Buddhism.
Fast-forward 800 years and there is a very different Buddhist landscape for the peasantry (and everyone else, really). Many new Buddhist sects arose during this time that appealed to commoners (especially the ones which offered simplified routes to salvation; see Pure Land Buddhism). Additionally during the Tokugawa, Buddhists began to educate commoners at temple schools for the first time en masse. During this period Japan's literacy rate was upward of 40% in males, comparable to contemporary Western nations. This is not to say that all peasants knew how to read, but certainly some of them had better educational opportunities than their 1050's counterparts (especially the more well off peasants).
Agriculture
Throughout these 800 years Japan's methods of agriculture evolved, especially as a result of the civil strife imposed on the country during the 16th century. These improvements diffused throughout the 17th century and generally led to higher crop yields, and the massive economic growth which eventually led way to the Tokugawa period proper.
These improvements would most likely mean your 1850 peasant was eating more rice than your 1050 peasant.
This is about the extent of what I have studied in regard to your question. Another complicated aspect is the change in government (namely from a "classical" Heian system to a warrior government featuring daimyo). However I lack the knowledge to definitively comment on any such changes, especially in regard to their impact on the common people. Hopefully someone with a better knowledge on the subject will be able to shed some light!
Sources:
Hane, Mikiso. Premodern Japan: A Historical Survey. Boulder: Westview, 1991. Print.
Hanley, Susan B. Everyday Things in Premodern Japan: The Hidden Legacy of Material Culture. Berkeley, CA: U of California, 1997. Print.
One of the major things that would be different was the food.
Food history is one of my favorite things to discuss and I've written extensive answers about it before but I'll keep it short for here.
One of the important things that would be different in the farmer's land and cuisine would be the inclusion of crops that had been brought from overseas, including sweet potatoes and pumpkins.
These were brought by European traders and introduced to the country a few hundred years before 1850 (along with other foodstuffs and new methods of cooking). While Japan already had native yams and squashes, sweet potatoes were an important crop that quickly became very popular to grow because of its safety as a food crop, helping farmers hedge against starvation if many crops failed.
Another difference between 1050 Heian Japan and 1850 Bakumatsu Japan was the inclusion of meat.
Japan in 1050CE was still under many prohibitions against consuming the meat of cattle, horses, and chicken, while they had only just (relatively speaking) seen the the restrictions on fishing lifted. That being said, wild bird and game like boar or deer were excepted from these rules and often provided an important supplement to Japanese diets during this period.
By 1850 in Japan, meat consumption had grown more common. Still not nearly as common as it is today, not even close. But domestic animal rearing with the intention to eat them had grown, and it was more common to find meat of animals, both domesticated or hunted, on commoners' dinner tables.
As a side note, 1850 would have seen the influence of trading both goods and ideas with European traders and cuisine, like many other things, had some influences. As mentioned before, imported crops had grown fairly widespread over the centuries since the first contact with Europeans, as had some forms of cooking, like cooking things in oil or fat.
Before this (and really even during this time) cooking things in fat or oil was very uncommon and almost all together unheard of in 1050 Japanese cuisine. But the modern Japanese cuisine of delicious fried tempura goodness directly derives from Japanese cuisine taking a note from European influences.
Another major difference was the architecture.
Japanese Heian architecture had taken a big inspiration from Chinese architecture. The best example of this was the very capital of Heian Japan (modern day Kyoto) was modeled after the Chinese Tang dynasty capital of Chang'an.
But of course, the rural countryside did not look anything like this.
Many houses in previous centuries were often dug partially into the ground and fixtures around and above the dwellings were often fixed with brick, stones, and leanings of timber.
By the time of 1050 Japan, there was a large shift to focusing on creating habitats out of wood and straw. Many dwellings were largely unchanged from the pit houses of previous decades, but they were now largely constructed out of more refined wooden material and roofed in rough thatching.
There were buildings that simply rested on the ground as well instead of dug into the ground, and these showed a similar shift of building material to wood.
This is what the inside of an average Heian house could have looked like (this and the pictures I linked to above are all reconstructions, not living examples of Heian homes).
By 1850 Japan, architecture had been refined a great deal. While thatching was still a popular choice for rooftops, the distinctive shingled roofs with wide eaves like so had popped up all over Japan.
In general, architectural techniques and the processing of materials in the service of construction had been developed and refined over the centuries into an art form. Sharp fitting angles and setting joints together without the use of any nails or external fixtures like lashing rope were standardized and prevalent in architecture everywhere.
Another important difference that could be noted at a glance were Shinto shrines and Buddhist temples. In 1050 Japan, many of these places were still using unpainted, natural wood but by 1850, the tradition of painting everything the distinctive red color was set in stone.
The last major difference was economic and infrastructural.
In 1050 Japan, the economy had grown weak and currency was incredibly hard to come by in rural villages. Virtually all transactions were conducted via barter and even government agents and employees would often be paid in goods rather than hard currency.
It was doubly hard for a farmer in the countryside to get their hands on any meaningful amount of minted currency.
But by 1850, Japan's economy was robust and ran on an extremely closely managed system of currency, backed by the national authority of the Tokugawa bakufu. While the rural countryside's struggle in obtaining meaningful amounts of hard currency continued, it was not nearly as markedly difficult as it was 800 years prior.
Barter continued to be a useful option for both farmers, traders, and travelers, but having currency as well as paying for services and goods using it were the norm.
Speaking of travelers and merchants segues nicely into the fact that infrastructure for travel was recognizably better. Roads were carefully watched and travel heavily restricted by the authorities, but the roads themselves were very well maintained for both the sake of commerce, military expedience, bureaucratic travel, and the obligatory avenues of civilian movement and migration.
Good roads came along with good bridges (or bridges at all!) as well as post towns. In Japanese, these places were called shukuba along major veins of travel. Shukuba brought with them travelers and trade, which meant they brought people and money.
Villages near active post towns generally grew more prosperous and further strengthened their connection to the region and other communities.
Your average village in 1050 Japan probably felt (and in reality was) much more isolated and apart from the rest of Japan than your average village in 1850 Japan. On the other hand, the average village in 1850 Japan was likely more fundamentally connected to the happenings in the region, especially economically.
Something as simple as 'farmers/tradesmen going to market' would be immediately noticeable.
Those are some of the biggest things off the top of my head.
Let me know if you have any more questions! Cheers!
