Burma is better as a substitute for Tibet than Nepal bcs
Let's get into this! (Speaking here as a prof of Southeast Asian studies and not in my role as writer at Friaxis)
"Tibeto-Burman" language is, sure enough, a category that encompasses both of those places, as well as other, smaller languages like Hmong. But how much faith should we put in these things? Other than a shared linguistic background, the two places are not terribly alike, and we're shaped often by our history, environment, neighbors, etc. more than our ethno-linguistic origins. I think a combination of those factors have led the (lowland, Theravada, Southeast Asian) Burmese to diverge pretty radically from the (highland, Vajrayana, Himalayan) Tibetans.
There's climate, for one, which has a profound impact on how people live their lives. Burma, being in the subtropical monsoon parts of Southeast Asia, is an intensive rice-cultivating place with all that entails -- large-scale centralized organization of rice agriculture, meaning that the accumulation and control of people is vital.
Burma, like Siam, Cambodia, etc. - had a model of kingship centered on the Cakkavatin - the divine ruler at the center of a charismatic sphere. As one got further away from the king, one got further away from Burmese control until influence kind of petered out (instead of dead-ending at a border). People in between - e.g. smaller ethnic groups such as the Shan, Lanna
khon meuang, Mon, etc. - would vacillate between such kingly centers (Ava, Yangon, Chiang Mai, Nan, Ayutthaya) or simply decide to create their own center (e.g. Kengtung). Tibetan politics weren't really like this.
Then, there's the matter of Buddhism. Burma is, like Siam and Cambodia and Laos, in the Theravada camp, whereas Tibet has its own particular brand of Buddhism (shared with parts of India and Mongolia). The monastic language in Burma is Pali, but not in Tibet.
Finally, there's the issue of the highlands. The high/low distinction is pretty strong in Nepal and Tibet as it is in Southeast Asia, but the kinds of people in high/low are rather different. In SE Asia, groups living up high were generally non-Buddhist and non-hierarchical, whereas lowlanders were strongly Indic-influenced and Buddhist.
At any rate, I think that drawing similarities here would be a bit of a longshot. Rather like claiming for Persia standing in for India, perhaps (don't want to get too much into unrelated comparisons).
For further reading, Edmund Leach's old essay "On the frontiers of 'Burma'" remains a classic, if a little dated. His
Political Systems of Highland Burma is still fantastic. Maitri and Michael Aung-Thwin's work remains a great study of lowland Burmese society, and something I go back to again and again. Stanley Tambiah's
World Conqueror and "galactic polity" works remain real classics in trying to think through how a "mandala" state would work (see also Clifford Geertz's
Negara). If I might suggest my own book on Chiang Mai, there's a chapter or two on ancient Siamese/Burmese/Lanna conflicts (
Ghosts of the New City, 2014).