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The New Kadampa Tradition (or NKT for short) is an offshoot group that broke away from the Gelug school. One of the primary areas of controversy between the NKT and the mainstream Gelug school is the position of a figure called Dorje Shugden, who among the NKT is considered to be Manjushri emanated as a spirit in order to keep the Gelug school pure from teachings from other schools. Among the NKT Dorje Shugden is propitiated as an enlightened being, but within the Gelug school now it is understood that Dorje Shugden is a worldly spirit only, and should not be treated as an enlightened being.
As a result of this split, the NKT is very insular, and will generally only read a selection of books written by their founder, Kelsang Gyatso, and in general are not considered to be part of the Gelug school any more due to Kelsang Gyatso being expelled from his home monastery of Sera Me, but their selection of teachings and practices are all drawn from the Gelug school.
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Currently I follow Theravada tradition, however I have been many times to NKT temples/meditation sessions and I also did a retreat with FPMT in Nepal (traditional Tibetan Buddhism that follows HH Dalai Lama), so I have been there...
Yes, there are some disagreements and controversy, but I will not write my opinion on the controversy as I want to respect all followers of Buddhism. If you search on google or youtube you will find many pages and even a BBC documentary about it. Most of the controversy is about the worship of a "Dharma protector spirit", the Vinaya in NKT and about their leader that claims to be a Geshe and FPMT doesnt seem to agree with it.
My experience:
In NKT temples I only found nice people and a very kind monk, but I left because of the library: 100% of the books there were written by their leader Geshe Kelsang Gyatso, that bothered me, I was looking for the suttas and the words of the Buddha, but could only find Geshe K. Gyatso, sometimes it made me feel like being part of a cult, so I left, but I repeat: I only found nice people there, no regrets.
My experience with FPMT was very good, the library was vast with many different authors, but again I left because I felt like Tibetan Buddhism was mixed too much with local culture and other religions (astrology, shamanism, tibetan book of the dead etc...). But once again: Only found nice people and great monks.
In Theravada I found what I was looking for, but do not take my opinion as something right, I do believe every path to Buddhism can be holy, it is more about what feels right for you.