Michael Jennings has a new post that talks about upper houses in Australia; unlike Canada (where, if I recall correctly, none of the upper houses remain except the federal Senate, which more resembles the Lords than either the Australian or American Senate in its powers and composition), five of the six Australian states still have upper houses, yet also have parliamentary governments, which tend to lead to weak upper houses.
My personal observation is that bicameralism works best when powers are symmetric; asymmetric bicameralism can quickly reduce one house, normally the upper house, to irrelevance. But, asymetric systems can be useful in a parliamentary system, provided the restraint provided by an upper house is seen to be legitimate.
Incidentally, the U.S. Senate, like the upper houses in most Washingtonian presidential systems*, does have slightly more power than the House — primarily, the confirmation power of “advice and consent.” However, most scholars consider Congress symmetric, and that is certainly the case in terms of the ordinary legislative powers of the two chambers.
* My spur-of-the-moment coinage to compare with “Westminster parliamentary systems,” to describe the presidential systems used in most Latin American countries and the Philippines, which are based on the U.S. system of separation of powers. (Nebraska wouldn't be a pure Washingtonian system, because of the lack of an upper house. This is the most egregious example, but most states depart from the Washingtonian model in certain respects.) Let's see if that one's as successful as “Lottroversy.”