I am by no means an expert and Chinese Buddhism is the one I know the least about when compared with Vajrayana and Theravada. But I did spend 7 months is a monastery in Taiwan and 4 months at the City of Ten Thousand Buddhas in California so I will share my impressions.
Somehow though Tibetan Buddhism has many cultural aspects to it I think the willingness of some lamas to leave aside those forms and relate to Westerners by immersing themselves in the culture has something to do with it. Especially the early "pioneers" like Chogyam Trungpa Rinpoche, Lama Yeshe etc.
The other major factor is that the target audience of the Tibetan lamas is Westerners in the vast majority of cases. Due to the situation in Tibet, many lamas feel for Buddhadharma to survive it must be transmitted successfully to the West.
The Chinese temples on the other hand often function as cultural centres for the Chinese diaspora. The cultural aspects can be overwhelming for people with no knowledge of Chinese language and customs. Many Westerners who I met at a Chinese temple where I stayed in Canada for a time specifically mentioned the dharma functions (fa hue??? forgetting...) as particularly alienating. Bowing in unison, trying to put the sash on the haiqing perfectly, and a very stern formal atmosphere are difficult for many to take. People feel uneasy and afraid to make a mistake (afraid to fart, as one man said).
On the other hand, I enjoyed the dharma functions and to my ear Chinese Buddhists chants are very beautiful. If the temples tried to give commentaries on the practices in English and make the atmosphere more casual, that might go a long way.
Another thing to mention is that many Westerners like to study in a linear, progressive fashion- similar to how they studies in school. In many of the Gelug centres (perhaps this is the case in other centres too), this is quite possible. One can begin foundational studies on progressive text like the Lam Rim or Bodhisattvacaryavatara to get a firm basis, and then seek teachings on tougher topics like Madhyamika, and take classes on tantric practices.
With the exception of the City of Ten Thousand Buddhas, none of the Chinese temples I have visited offer a complete, in-depth study program with qualified teachers in English, other than very brief introductory courses. Even for the Western born Chinese kids, many of them told my they found the sutra lectures interesting but felt they were very piecemeal, and it was hard to develop a firm knowledge.
Tibetan lamas are in general more casual and approachable than Chinese masters. While a Chinese bhikshu or bhikshuni might consider it inappropriate to appear in photos holding babies with an arm around the student, for most Tibetan lamas this would not be a problem. The emphasis on being "chuangyen" or dignified is what allows the Sangha to be respected in the Chinese community, but ironically to many Westerners it seems stiff and unwelcoming.
That being said, Tibetan Dharma centres are at times also quite unfriendly, as mentioned in previous threads.
That's my first two points. More later
In order to ensure my mind never comes under the power of the self-cherishing attitude,
I must obtain control over my own mind.
Therefore, amongst all empowerments, the empowerment that gives me control over my mind is the best,
and I have received the most profound empowerment with this teaching.
brtsal ba'i bkhra drin