Daoism, as you might know, has very old roots in Chinese society and history, much like Confucian ideas. These ideas are considered part of a cultural history and traditionally Chinese, and as such, their traditions and values come up quite often in scholarship and dynastic governing. When Theravada Buddhism was brought to China, it started first as a small, court contained practice. It was something that was curious and interesting, but still quite foreign. Eventually, Buddhist ideas started to take hold and it became a popular religion within China (it seems that it had taken hold of the Xiongnu earlier than the ethnic Chinese from documented encounters. Exposure to Buddhism, then, would not only have come from traveling monks but additionally from contact with Xiongnu raiding and trading parties).

Now that we've established a bit of a background, the important difference between the two of them for the purposes of this question is that Buddhism included a monastic lifestyle while Daoism was rooted in the ancient traditions, including things like ancestor worship and focus on family. The Tang themselves were kind of split between the two of these worlds: they claimed to descend from Lao Zi (the Li family that were the Tang dynasty, that is) and they also encouraged Buddhist monasteries. One of the Tang policies was the exemption of Buddhist Monasteries and their land from taxation (similar to the European policies you may be familiar with). This was exploited quite often by the landowning aristocracy who would give parts of their estate to Buddhist control so as to avoid taxation, and then provide a portion of the boon from the land to the monastery .

Now, we finally get to the direct address of your question: what was it like between the Daoists and the Buddhists? I believe Bentley's Old World Encounters has a decent account of this story, but around the early 9th century CE, there was a finger bone, claimed to be from "The Buddha" (Siddharta), that came to be circulating around "on tour" in China. A figure by the name of 韩愈 (Han Yu), a kind of philosopher and poet (more accurately, a 君子, Jun Zi) during the Tang dynasty who was strongly in favor of Confucian ideas and strongly against Buddhist ideas. He ended up writing a document criticizing Buddhism and the worship and awe of the finger-bone that was circulating around China. He wasn't a big fan of Daoism either, but one of his major arguments was that at least Daoism was a Chinese originated ideology. Eventually, there was a short-lived ban on Buddhism and the monasteries altogether.

As to what the Buddhist views of Daoists may have been like, one part of the Journey to the West (西游记, xiyouji) that you mention reflects a practice that was an interesting part of Daoism. The part I'm referring to is the implied relations with evil spirits. Whereas Buddhism teaches that permanence is a lie and giving up worldly possessions helps to emphasize that no one and nothing is permanent, there is an element of Daoism that emphasizes the chasing of immortality in a physical sense. This is the concept of Xian (仙) which may be more familiar as Zen in Japanese. A common part of this practice was to take "medicines" that would create an altered state of consciousness in order to achieve some enlightenment through communication with the spirits, who would then prescribe an additional recipe for a greater effect.

I can't comment on why Wu Cheng'en would have portrayed Buddhists negatively, though I would say that there are plenty of other examples of Daoists consorting with evil spirits elsewhere in medieval Chinese literature. Daoists (in the sense of magicians) are portrayed in quite varied ways overall, sometimes evil, sometimes good and sometimes simply bizarre. I wouldn't read too much into individual examples.

However, there might well be something to what your getting at. Buddhism grew rapidly during the early Tang dynasty, and monasteries became enormously wealthy, in large part because of the ingenious practice of allowing people to buy karma, through which they acquired large estates, serfs etc. Although Buddhism had enjoyed an immense degree of state support during the early Tang, in 845 Wuzong ordered many of the monasteries closed, forcing the monks back into lay life. Chinese Buddhism never really regained the prominence it had before the repression. I don't think the persecution was in any way motivated by Daoism though.