I mean, they're both true. Though I suppose "victory" is more or less in the eye of the beholder here, and everything that happened in the, basically, immediate decades after the war pretty much nullified the peace treaty between Nepal and the Qing.

The War had its origins in the devaluation of silver in the Tibetan marketplace by Nepali merchants and was triggered over a turf dispute from the Shamarpa Lama who fled Lhasa for Katmandu. Since there had already been tension regarding the Tibetan devaluation of silver, the Nepali King Bahadur Shah decided to use the turf dispute to return Shamar Rinpoche to his throne, and exact the tribute from Tibet directly (i.e. by force, raiding Lhasa for all it was worth).

The Gorkha invasion of 1788 went pretty bad for the Tibetans, who pretty much sued for peace immediately. The 18th Century did not go well for the Tibetans up to that point anyway. Theoretically, a half century should have been more than enough time to get over the murder of the 6th Dalai Lama, the murderous campaign of Lhazang Khaan, and the attempted genocide by the Dzungars, but frankly the Tibetan government never got their proverbial shit together and politically relied on the nominative support of the Qing. When the Jesuit missionary Ippolito Desideri visited Tibet in the 1720s, he was under the impression that Tibet was a vassal of China.

This was not strictly true (if it were the case, the Qing would have already had a garrison in Tibet and would have repulsed the Gorkhas immediately). However after the murder of the 6th Dalai Lama, the Qing did put the reborn 7th Dalai Lama at the front of an army and marched him to Tibet, cleared Lhasa of the Dzungars and kept the peace while things settled down. Then a former lieutenant (at least he was a Tibetan and not a Mongol(!)) by the name of Pholhanas (pronounced P'o-l'ha-nay, not Pole-hah-nass) tried to start Tibet down the path of a secular monarchy, but similar to Cromwell's experiment with primogeniture, it lasted only 1.5 generations before the Tibetan government slipped back to essentially absolute control of the Dalai Lamas, with the Qing Emperors taking the role of the Mongol and Qoshot Khaans who maintained a hands-off policy towards the Dalai Lamas' Lhasa activities (with the exception of course of Lhazang Khaan).

After the 5th Dalai Lama, however, the Dalai Lamas would maintain very little centralized control of Tibet, or even Lhasa, frankly, until the 20th Century. The 7th Dalai Lama was more interested in religion than he was in politics, and his ambitious father was much more involved in controlling things than his son was (from what I understand, though I gather this is always a controversial issue). The 8th Dalai Lama had to undergo a crisis of confidence because of an old prophecy in the Book of Kadam which said that there would only be seven Dalai Lamas. The 8th is reported to have said, "There are many who call me Lama, but not King, and the others call me King, but not Lama." (Side note, this is probably why the current 14th Dalai Lama regards the current lineage of Dalai Lamas as two lineages, one from the first to the seventh, and his current lineage which spiritually begins with the 8th to his current incarnation, even if the title passed seemlessly from the 7th to 8th).

Anyway, the 8th was the last Dalai Lama to preside even remotely over the Tibetan government until the 13th would declare independence from China in 1912. Of course, the Tibetan government was hardly centralized at that point, with the Panchen Lamas still running most of their show in Shigatse to the west of Lhasa (when George Bogle visited Tibet in 1776, still during the 8ths regency, he dealt mainly with the Panchen Lama and was under the impression that any deal between Tibet, China, and the East India Company would go through him, indeed, it seems a foregone conclusion to us now, but throughout the 19th Century, the Panchen Lamas held much much more de jure power than the Dalai Lamas who kept mysteriously dying young).

So with no real government centralization, no semblance of unity among the society that prized itself on freedom and a lack of violence (though this is of course debatable, I've written about it before if you'd like links) there was certainly no Tibetan army and wouldn't be any until 1920. The Tibetan government had been relying on (what we might call) feudal levies and the Mongols and Qoshot as their military arms. And with both of them gone, and very few feudal lords ready to defend a government they weren't too keen about in the first place (the importance of central stability), the Tibetan Army was pretty pathetically out of luck.

Meanwhile, the Gorkha were arguably at their pre-British peak. They'd been expanding their influence in all directions across the Himalayas, had been raiding into India as the British were inducing chaos from their base in Calcutta, and in a few years would fight the British to such a brutal standstill that the East India Company would basically turn around and try contracting them for future wars (which they very famously have participated in down to the present day). Not only that, the Nepali King had amassed a lot of power, but that's just pretty obvious when compared to the chaos going on in Lhasa.

So when the Tibetans stopped paying the tribute originally agree upon, the Nepalis figured, "Welp, might as well go with Plan A" and re-invaded Tibet, aiming directly for Lhasa.

The Tibetans, who had managed to attract the attention of a Manchu representative at that point, then pleaded for a Chinese army to repel the Nepalis. A Manchu responded saying "Yep" and sent a force that not only repelled the Nepalis, but pushed into Nepal, fighting them to a standstill on their own territory. From what I've read, it's a bit unclear how willing the Manchu were at that point (anything from "the Himalayas are dangerous and they wouldn't dare go all the way to Katmandu" to "oh hell yeah they totally could have") but what ended up happening was a peace treaty that theoretically made Nepal a vassal of Qing China, bringing Nepal as well as Tibet into the Chinese tributary system.

The winner in this scenario was clearly the Manchu. They militarily defeated Nepal, even if they didn't secure a complete surrender of them, they by definition accomplished their military goal to secure Tibet, and wound up in control of their geopolitics, local governance, economy, and had an army garrisoned there until the Revolutions that overthrew the Qing in China (1911) and Tibet (1912). The Tibetans, I would say, more or less lost since they lost sovreignty of their country and never really got it back. As a consolation prize, the dispute that triggered the whole event with the Shamarpa Lama ended with the Tibetans burying the Red Hat he was named after (Zhwa dmar pa = literally "the one with the red hat") at a cross roads so everyone passing through would step over it (this is considered by some a fate worse than death, as the "seat of the soul" is at the top of the head, and it's often said among Tibetans something along the lines of "Better to lose your head than your hat"). The Shamarpa's incarnations were forbidden to be relocated until after 1959 when he was located and revealed in exile (and they still claim that his followers located and named him during the years his rebirth was banned from recognition, making the lineage continuous). Finally, the Nepalis were certainly the winners in that they maintained their sovreignty and wound up in that sweet-spot of "in the Raj, but not of the Raj" when the British intensified their colonial Empire in India. That's a story for another time though. Regardless, after the war Katmandu certainly had her hands full dealing with events to the south, and while Tibet remained an unruly child in the Qing Empire (probably was one of the reasons they were glad not to have to worry about ruling the Nepalis for the next century while they were at it, too) events in the south and east (the Opium Wars, Taiping, Tianjin, etc.) would make enforcing the fact that technically Nepal was supposed to have the same status as Tibet (i.e. entirely controlled by Qing authority) impossible.

So it would not surprise me that Nepalis claim it as a victory. They maintained independence, and never had to surrender. As for the silver, I imagine Tibet's annexation into the Qing Empire and the control of her economy from Peking probably made the issue moot, though I'd need to check Petech's China and Tibet in the XVIIIth Century to be sure.

tl;dr: China and Nepal signed a peace treaty. No one surrendered. Tibet definitely lost because they lost their sovreignty and suffered under Manchu imperial control for the next century and a quarter, while the Nepalis technically agreed to the same status, but the ensuing chaos of Colonialism's Act 2 made the treaty impossible for the Manchu to enforce in Nepal, so they got the better deal out of the Peace Treaty.

Sources:

Sam van Schaik, Tibet: A History

F. de Fillippi, An Account of Tibet

Glenn H. Mullin, The Fourteen Dalai Lamas

Kate Testcher, The High Road to China

I'm probably forgetting a few, but I'm happy to answer follow-up questions.