Samuel explains one example:
This Protestant model formed a template that was repeatedly applied by Western scholars to Asian religious traditions. At the same time, it provided a model in terms of which nineteenth and twentieth century Hindu and Buddhist reformers, from the Brahmo and Arya Samaj down to the Mahabodhi Society, attempted to reshape their own religious traditions. Buddhism, which had its own narrative of teaching and decay, fitted the model particularly neatly. The Buddha could be seen as a humane religious reformer on the model of Jesus, teaching through parables and other simple and straightforward means. In this perspective the Buddha became a kind of Christ figure reacting against a legalistic and caste-bound Brahmanical priesthood, the Hindu equivalent of the Sadducees and Pharisees of the New Testament account.
Geoffrey Samuel, The Origins of Yoga and Tantra Indic Religions to the Thirteenth Century (New Delhi, India: Cambridge University Press, 2008), 16.
There's a few more aspects I'd like to discuss:
- The view that the Pali canon best represents an original Buddhism via a historical Buddha, and that this is worth adhering to as a pure or authentic Buddhism (getting to the "true teachings" of the Buddha, not unlike getting to the original teachings of Christ).
- The new exclusive nature of Buddhism, whereby self-identifying Buddhists are actively discouraged from participating in non-Buddhist religious activities.
- In some modern Buddhist traditions a distaste for rituals, 'superfluous iconography' and archaic liturgy (Protestant influences).
- In some traditions, centralized administrations with a key figurehead and his or her elites in charge of all major decisions and policies with underlings expected to show obedience (Catholic influences).
I think the most pertinent influence from Christianity has quite possibly been the second on the list: the new Buddhist self-identity where exclusivity is now seen as important and worth emphasizing. Of course in the past "Buddhists" existed, but as we know even today were often readily able and willing to participate in all manner of other practices and ideologies, and even incorporate them. Christian-like exclusivity for Buddhists is probably a fairly new development in most cultures.