I just answered a question like this two weeks ago, but I'll summarize here also:

Tibet was under Manchu control from 1792 to 1912 when simultaneous revolutions in China and Tibet gave rise to the Republic of China in the east, and a independent Tibet in the west. In the summer of 1914, representatives from the Chinese and Tibetan governments met in Simla, India, with the British to hammer out the exact relationship between the three powers. The Chinese at the time, regarded Tibet as theirs, akin to an imperial possession. This view was widespread in China. The thought process from a Confucian worldview translating into a western-oriented and Communist one is well documented in Smith's Tibetan Nation. However, the British were eager to keep their own influence over Tibet, keep the Russians out of it (Russo-phobia for better or worse, really infected British thinking around Tibet at the time) and solidify the northern border of India (in their favor.) They managed all of these goals, and the unprepared Chinese (who assumed they would be carving up Asia with the British) left disappointed. The Tibetans, who came prepared, presented their arguments for their eastern border with volumes of books containing tax and tribute documents, whereas the Chinese had only their word and imperial design.

I mention this primarily because it shows the Tibetans had a tax structure extending as far east as Kham (today's Sichuan Province). And in the '20s, the Dalai Lama's attempts at modernizing the Tibetan army would bear fruit in victorious campaigns in the Amdo region (modern Qinghai).

However, the government system that the Dalai Lamas claimed to be the head of was called the Ganden Phodrang, so called because it was traditionally run out of Ganden Monastery in Lhasa (Phodrang being "Palace," a common epithet for Monasteries and Dzongs). The Ganden Phodrang rose to power in 1642 with the victory of the Qoshot Mongols over the Tsangpa King in Lhasa, seating the Fifth Dalai Lama in Lhasa, was vassalized by the Manchu partly in 1720, and completely by 1792, became completely independent in 1913 with the 13th Dalai Lama's Declaration of Independence and the Tibetan Revolution, was superceded in 1950 with the Communist Invasion, and was driven into exile in 1959. After that it undertook many changes and now exists as a purely religious body if it can be said to exist in any form at all.

One problem that histories of this time period have (especially regarding English-language texts) is that they tend to focus on the Lhasa region. The reasons for this are obvious (Lhasa is the largest city, the capital, and the center of Tibetan life generally speaking) but present a comprehensively biased view of Tibetan society. Lhasa, being the traditional seat of the Dalai Lamas and his government, was reigned more or less like an absolute monarchy. What the Dalai Lama said, well, pretty much went as directed. Though it would be false to believe that he was universally obeyed, loved, or listened to (see the above link) and disobedience, rebellion, and assassinations against the Dalai Lama and his government are well recorded.

Outside of Lhasa, the Dalai Lama's society is quickly reduced to a patch work of traditional ways of living. As mentioned earlier, there was certainly a strong presence of the Ganden Phodrang government in Kham and Amdo, but the tax and military structures there were islands of his order in a sea of traditional life. Amdo is the home of the militaristic and radically free Golok tribes who mocked both the Chinese to their east, and the Tibetans to their south (people in Amdo and Kham don't always refer to themselves as "Tibetan," which itself kind of proves the point I'm making about how loose Central Tibetan control really was) as subservient, whereas they, the Golok, bowed to no man and were free.

The Golok are probably the most extreme example, but Heinrich Harrer in the 1940s details a rather frightening encounter with Khampa herdsmen (/highway robbers) who made a living on the track just to the south of Lhasa by robbing and murdering travelers, well outside the realm of the Dalai Lama's control.

And then, of course, is the issue of the monastic estates, which is usually what is referred to when we talk about "feudalism" in Tibet. To say that Tibet's monastic estates were huge, wealthy, powerful, and at times harsh is a statement of fact. Their wealth and power was, however, by design as the Manchu sought to pacify Tibet (which was prone to rebellions half way through the 19th Century) by generously patronizing the monasteries and encouraging ordainment to remove potential fighters from the population.

To call this "feudal," however, is to miss the point entirely of how Tibetan society function, and usually carries the implicit assumption (look at literally any Reddit news thread on Tibet) that Tibetans want to go back to that society. In the above link I detail how the 13th Dalai Lama (the current one's predecessor) made many efforts to try and modernize Tibet. Those efforts usually involved an expansion of state control and authority, but were primarily directed against the monasteries and their "feudalism," if it could be called that (which I would argue, it can't be).

Tibetan society pre-1950 was certainly primitive in comparison to her neighbors, but this was a matter of economics, access, and an element of political infighting. The problems with calling Tibet "feudal" is that it carries a series of assumptions both about feudalism itself and those who traditionally refer to it as such (Chinese Communists), whose political legitimacy depends on the term.

In the sources I list above, which I'll reproduce here, you'll notice several Tibetan made works that are very well done (Shakabpa and Shakya in particular) that cover the good and the bad of Tibetan society pre-1950.

Tibet: A History by Sam Van Schaik

Tibetan Nation by Warren W. Smith

Dragon in the Land of Snows by Tsering Shakya

Tibet: A Political History by Tsepon Shakabpa