To paraphrase an answer I once heard from the POV of a Gelugpa Lama:
In Tibetan Buddhism, we guide the student to the top of the mountain using well-trodden and safe paths, around and up to the top. Zen goes right up the north flank.
Generally speaking, both are categorized as Mahayana, but there is much more ritual and esoterism in Tibetan Buddhism, it schools mostly subcategorized as Vajrayana than there is in Zen, which is often called the Sudden Teaching and subcategorized as Subitism.
One of the main reasons for this difference is the local culture into which both forms of Buddhism were imported from India and the related chronology.
In Tibet, the Buddhist texts were first translated from Sanskrit around the 8th century, and the wordings used to translate many of the Buddhist Sanskrit principles were based on local concepts from the Animistic Bon religion. In the texts that came to Tibet around this time, Indian Buddhism had transformed Buddha into a cosmic figure. This resulted in Indra, the Thunder God being absorbed by Buddhist spiritualism until Indra’s thunderbolt, known as Vajra, a symbol of the power of nature was transformed into the Buddha’s diamond scepter, representing spiritual supremacy and the power of compassion.
In China, the first Buddhist texts were translated much earlier, during the Han dynasty around 200 BCE, and influenced by the local Taoism. The texts central to Ch'an (Zen) only came to China around the same time Buddhist texts came to Tibet, but by that time the core Buddhist concepts were already part of the Chinese vernacular and had already been associated with core Chinese principles such as Tao. The essence of Zen is found in the
Flower Sermon, in which the Buddha simply held up a Golden Lotus instead of preaching with words. The disciple Mahakasyapa, whose insight of understanding this message was shown only by a quiet smile, was designated his successor. The Chinese found this teaching to perfectly match with the opening verse of Lao-Tzu's Tao Te Ching:
The Way that can be followed is not the eternal Way. The name that can be named is not the eternal name.
Please keep in mind this is a very generic answer. If you would look at the establishment and evolution of individual Tibetan or Ch'an/Zen schools, a very different pattern emerges, and of course, there were new or refined concepts introduced in both schools. A good example of this would be Nagarjuna's Madhyamaka.
For a detailed comparison, see Presentation on Zen and Tibetan Buddhism