You can take a look for yourself in this graph:
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It's not surprising that there's more House bills, since there's twice as many legislators in the "People's house". If there's any surprise, it's that the Senate averages not 50 percent of the House's total, but just over 75 percent.
The work of compiling this chart suggested a route for further inquiry, so I went back into the Legislative Research Council's records and compiled the number of bills that have passed in recent years:

The average from 2003 through 2009 is 158.57 House bills passed and 121.71 Senate bills pased.
Simple division suffices to combine these two charts:

Some really interesting stuff in that graph. First, the average success rate during Rounds' tenure is even for both houses — 57.28 percent for House bills and 56.66 percent for Senate bills. But that average conceals huge variance, especially on the House side. While the Senate's success rate varied from a low of 52.51 percent in 2007 to a high of 62.39 percent in 2004 (a spread of 9.88 percentage points), the House swings from a low of 47.18 percent passed in 2003 to a high of 71.43 percent in 2008. That's a spread of 24.25 percentage points, or almost two-and-a-half times as much variance as the Senate.
New classes of legislators started in the odd-numbered years. Could the big swings be due in part to legislators getting more experience in their second year?
House lawmakers passed an average of 53.55 percent of their bills in odd-numbered years and 62.26 percent in even-numbered years (though if 2008 is an outlier that may exaggerate the difference. The average success rate for the House in 2004 and 2006 was 57.68 percent.)
Senators passed 55.85 percent of their bills in odd-numbered years and 57.74 percent in even-numbered years.
The data sample here is small enough I'm not willing to make any judgments about whether those differences are statistically significant.
2009 was my first year covering the Legislature, so I don't know what may have been going on in, say, 2003 in both houses, or 2008 in the House.
The other interesting thing in that graph is that the Senate was more successful than the House in 2003, 2004 and 2009, and less successful in 2006, 2007, and 2008. The two were basically tied in 2005. Again, I'm not sure if that means anything or not, but it's interesting.
EDIT: You can download my spreadsheet here.


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