The LDP was born of a merger between two conservative parties in the mid-1950's, the Liberals 自由党 and the Democrats 日本民主党. As such, it has never had an all-encompassing goal or ideology, unlike the Kuomintang, with its initial desire to "retake the (Chinese) mainland" and its present effort to return Taiwan to the Chinese fold and thwart Taiwanese independence drives. Rather, the LDP has always been a collection of factions held together by the prospect of power. In fact, in the old days of Japan's multi-member electoral districts, party members competed against themselves more often than they did against candidates from opposition parties. Unlike the KMT, the LDP has never considered itself a part of the fabric of the state - the Japanese nation/state has existed long before there were Liberal Democrats, quite the opposite from the Republic of China 中華民国, which owes its continuing existence to the KMT (and vice versa).
The biggest difference between the two parties, however, is how they managed to stay in power for so long. For the KMT, this meant the imposition of martial law 戒厳 until 1987. Political opponents were imprisoned, tortured and executed in great numbers during the years of the White Terror (http://en.wikipedia.org/wiki/White_Terror_%28Taiwan%29). After Taiwan's democratization, the KMT was able to remain in control thanks to its deep penetration into local political structures (unlike in Japan, where politics at the local level is organized quite differently). The Democratic Progressive Party 民主進歩党 was only able to win the presidency in 2000 thanks to a split in the Blue camp, and barely won the 2004 race. The KMT refused to accept its new status at the opposition party, and attempted to destabilize the DPP government through impeachment attempts, legislative stonewalling, violent street demonstrations and backroom negotiations with the Chinese Communist Party 中国共産党, finally regaining the presidency in 2008 (and is now in the process of using any and all means at its disposal, constitutional and otherwise, to ensure it remains in power in the future, but that's another story).
It is true that the LDP benefited in the past from an electoral system that gave a disproportionate share of votes to rural districts (a traditional bastion of support for the Liberal Democrats), not to mention an ineffective opposition (meaning for a long time, the Socialists 日本社会党, who seemed to be content being the permanent Opposition). The main reason, however, for the LDP's long ride in the saddle was quite simply that it delivered the goods, economically speaking, from the end of the Korean War 朝鮮戦争 to the bursting of the bubble economy バブル経済 at the start of the 1990's. Japanese voters always had the opportunity to remove the Liberal Democrats from power, but chose not to do so, as long as incomes were rising and affluence was increasing. It was only when the economy began to stagnate that they turned against the LDP. The LDP was out of power for a nine-month period in the early Nineties, and had only been able to stay in control since then by forming coalitions (including with the Socialists at one point!), with the 2005 election being an anomaly due to Junichirō Koizumi's 小泉純一郎 personal popularity. When the end came, staring with the loss of the upper house 参議院 of the Diet 国会 in 2007, and followed by yesterday's annihilation at the polls, the LDP bowed out more or less gracefully, as any mature political party should. Say what you will about the Liberal Democrats, for all their faults, they have generally played by the electoral rules and followed the democratic process.
It's often forgotten that Japan had the only democratic political system in place in East and Southeast Asia from the end of the Second World War until the late 1980's. For all its faults and abuses of power, one shouldn't overlook the contribution made by the Liberal Democrats to Japan's postwar political development and yesterday's possible birth of a true two-party system. It's unfortunate that there are few, if any, lessons to be learned, or conclusions to be drawn, from what happened to the LDP on Sunday in regards to the current state of politics in Taiwan.