I can only speak as a Taiwan native, and I can't say anything about Korea, but Taiwan's relationship with Japan is pretty complicated and nuanced. Yes, the Taiwanese were taxed more, and forced to speak Japanese, and killed without reason, but we also got significant advancements in education and other areas because of Japanese influence. Also, I think much of the enmity (because there is Taiwanese enmity towards the Japanese just as there is goodwill) is traced to events such as the Rape of Nanjing. Though it happened in China, it occurred before the Chinese Civil War and thus affected a lot of the "second-wave" families that have since migrated to Taiwan.

Japan had different colonial policies for Korea and Taiwan for some time, although these policies changed with the political climate and sometimes with the very whims of colonial administrators. In general, one aspect was how the Japanese view of Korea vs. that of Taiwan. Taiwan, an island with a diverse population of around one-forth of that of Korea, was thought to be easier to assimilate to Japanese rule than Korea, which had a larger, more homogenous population. Around the end of World War I, Japanese policy in Taiwan shifted from that of colonial economic exploitation along the lines of other imperial powers to "Douka" or "Assimilation". It was thought that Taiwan could be an extension of the Home Islands on the line of the Ryukyu islands (like Okinawa) and so to a large extent the Japanese started encouraging people to assimilate to Japanese rule. Those who converted to Japanese (by speaking Japanese, adopting Japanese names, and having a nice placard in front of their house saying "This is a Japanese household") were rewarded, either with more food, better education, and so forth. The Japanese government was also more lenient when it came to popular demonstrations-local limited democracy in the form of assemblies was gradually given more power, and the Taiwanese had representation in the Japanese parliament.

This contrasted sharply with the contemporary Japanese policies in Korea. Unlike Taiwan, the Koreans were not only not encouraged to change their name to Japanese, but were in fact forbidden to do so until 1939. The Japanese efforts in Korea amounted to one primary purpose: Japanese supremacy. The Japanese revived the Korean alphabet, Hangul, and imported Japanese-style public education into Korea. The goal of using Hangul was to educate the local peasantry, who at the time were mostly illiterate. By educating the peasantry, the Japanese sought to break the remaining power of the Korean nobility and thus enhance the Japanese position. These Koreans were taught not only basic reading and writing, as well as trade skills, but also what amounted to Japanese brainwashing. They were taught a revisionist version of history which essentially stated that because of so-and-so reasons, Japan has always been the lawful ruler of Korea, and you Koreans should accept it peacefully without resisting us. To a large extent, it worked, although there were plenty of uprisings and protests against the Japanese, such as the March 1st independence movement which was put down bloodily by Japanese troops. It got to the point where the Japanese turned a blind eye when the Koreans were inflamed by anti-Chinese sentiment and rioted in 1931 against Chinese residents of Korea, as it was not against the Japanese rule.

By contrast, aside from the "Wushe Incident" (where a group of Taiwanese aborigines of the Wushe tribe, offended by a Japanese officer's actions, massacred a Japanese school during a field day), the Japanese were viewed as being more benevolent in Taiwan. Shrewd diplomacy and policies by the local administration pitted the local ethnicities against each other (Han, Hakka, Aborigine, and others) allowing the Japanese to seem like a welcome intermediary.

This all started to change in 1937 with the rise of the militarist government and the start of the Sino-Japanese War. The military saw both Taiwan and Korea as useful grounds for recruitment and military production, and much harsher assimilation policies were implemented. The bans on changing names in Korea was removed, in fact it became, if not outright mandatory, highly encouraged. These efforts were not without success-many Taiwanese and Korean men ended up serving in the Japanese military, and in fact several Koreans ended up as generals in the army. Even those that were not high rank soon rose to power after the war-as an example, Park Chung-Hee, one of Korea's most well known leaders, was a lieutenant in the Kwantung Army.

During this time, however, institutional discrimination, despite the official stance that all were "subjects of the Emperor," reached an all-time high. Japanese nationalism was fanned in the schools, and those who were not of Japanese descent were scorned-there were several instances were Chinese studying in Japan were spit on, and several anti-Chinese riots broke out as well. This discrimination was also present in the colonies, most notably in the form of such institutions as comfort women. These sorts of behaviors severely damaged Japanese credibility in Korea and Taiwan.

However, as keyilan mentions, the post-war period had different effects. While the Koreas were split into two and fought a war, although both sides were officially ruled by Koreans, Taiwan was forced to become the refuge of the Kuomintang Republic of China government, as well as a massive influx of refugees who were not influential enough to immigrate to the US or rich enough to go to Hong Kong. Extremely unpopular reforms by the KMT, such as land reform, stripped the Taiwanese of their property and of their rights, fostering significant anger and resulting in the 2-28 incident, which was violently put down by the Kuomintang military. As you would guess, this made life under Japanese rule seem great by comparison.

But that wouldn't explain the whole story of why for the most part the Taiwanese as a whole have a better opinion of the Japanese. There were still a large number of immigrants from mainland China who had suffered from the Japanese invasion. For these immigrants, their anger was shifted to the Communists on the mainland. Chiang Kai-Shek, the leader of the KMT, was a firm believer in the importance of loyalty, having picked officers loyal to him over those that were probably more qualified in the past, led a reform in the Taiwanese education system to basically brainwash the population into anger against the mainland. The new population was essentially being trained for the day when the KMT would retake the mainland from the communists, and thus a lot of the anti-Japanese rhetoric fell by the way side. On the other hand, while Syngman Rhee suppressed prosecution of so-called "chinilpa," or Korean collaborators with Japan, the violent legacy combined with Korean nationalist fervor to create a more negative attitude about Japan, and Koreans tended to blame the division of Korea not on the "other Korea" but foreign influences in the form of the US, USSR, and Japan.

Something worth keeping in mind about Taiwan, in addition to all the other sides of this question and all the other reasons for the current dynamic between Japan & Taiwan and Japan & Korea, is that the KMT really botched things in Taiwan when they arrived in 1945. However oppressive the Japanese rule was to the average (non-aboriginal) Taiwanese citizen, it was a much softer blow than what they faced with the KMT takeover. Upon their arrival things were immediately put in a state of disarray, and it only took a couple years before violent anti-government protests were happening, leading to the 228 Incident. So part of the difference in opinion has a lot to do with relativity, and Taiwan having a much more recent bout of oppression that's fresher in people's minds. It wasn't until the 1990s that people even began speaking publicly of the events.

An additional and (I feel) significant factor as far as Korea is that Japan had a very complex view toward the Korean. On the one hand they were primitive and subject to the same sorts of Orientalist ideas that the West has traditionally held for the Near and Far Easts, but then on the other hand they were seen as, in a sense, a Japanese people with a common ancestor. Japan held a mixture of distaste and fascination toward the Koreans, while at the same time feeling the need to break Koreas ties with China which until this point had been the greatest cultural influence.

You'll surely get a more comprehensive answer soon, and hopefully someone like /u/AsiaExpert will show up to take care of that.

edit: typos