Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I even say who wrote them. If you have more recent summaries to add to this collection, send them my way I guess. Sorry for the ads; they cover the costs of keeping this online.
Sartori. 1994. Neither presidentialism nor parliamentarism. In The Failure of Presidential Democracy, eds Linz and Valenzuela.
Semi-presidential and semi-parliamentary systems are superiors to their pure-presidential and pure-parliamentary counterparts because they avoid the structural gridlock and feeble and inconstant government inherent in both. Political context (party system, etc.) also plays a role.
Must have all three: (1) head of state is popularly elected; (2) parliament can neither appoint nor remove the government; (3) the head of state is also the head of the government (cabinet).
Must have all three: governments are appointed, supported, and (if necessary) dismissed by the parliament.
Pure-Presidentialism is structurally damned; Recent Congressional-Presidential (with the exception of Clinton) travails prove it. Pure-presidential regimes rarely survive, and those that do (US, mainly) cease to function during periods of divided government--which the US has experienced for several years now. [The more recent lit on US divided government would disagree.]
Also, videopolitics (modern candidate-centered politics) increases the risk of electing a doofus because voters are likely to vote with their passions instead of the reasons.
Valenzuela defends parliamentarism over presidentialism by claiming, "The crises of parliamentary systems are crises of government, not regime" (as opposed to presidentialism, where deadlock leads to a coup or other crisis of democracy). However, partisans of presidentialism claim that (pure) parliamentary systems are immobilist and inefficient.
Electoral systems color party structure and governmental stability. And the party structure influences which of these flavors is best. The British system requires a two-party system with strong discipline, for example.
A functioning parliament is dependent on well-disciplined and cohesive parties. Parliamentarism can't be foisted on a system with incompatible parties. Thus, Brazil's recent  talk of switching to parliamentarism is misguided, since its parties have almost no role. Politicians switch party frequently and frequently defect against the party line.
Research on similar subjects