By decision of the electoral commission, Taiwan will move to concurrent elections for president and legislature. Robert Elgie has some details, and concludes by noting:
The other semi-presidential democracies with scheduled concurrent elections are Mozambique, Namibia and Peru. The last concurrent elections in Romania were in 2004.
Taiwan’s move makes sense, as did Romania’s–in the other direction–before it.
With the Taiwanese move, the remaining cases of concurrent elections are of the president-parliamentary subtype of semi-presidential democracy. Romania, on the other hand, is premier-presidential. ((Definitions: A semi-presidential system has a popularly elected president alongside a premier (prime minister) who is responsible to the legislative majority. Under premier-presidentialism, that responsibility is exclusive: the president is not granted constitutional authority to dismiss a premier or cabinet. Under the president-parliamentary subtype, the president has constitutional authority to dismiss a premier, who thus (along with the rest of the cabinet) must maintain the confidence of both the elected president and the majority of the legislature.))
I would argue that the more the formal rules of a semi-presidential system lean towards presidentialism, as in Taiwan, the less it makes sense to have nonconcurrent elections, which increase the odds of an opposition-dominated legislature. For premier-presidentialism, on the other hand, it is logical to increase the (potential for) independence of the premier by making legislative elections separate temporally from presidential.
It appears that constitutional reformers agree–at least those who have recently reformed the electoral cycles in Romania and Taiwan!