Which was more significant: the Gold Rush in California or in Alaska?
It should be pointed out that Alaska was already a U.S. possession at the time of the gold strike there. Although it drew many people to that area, it had little effect on the U.S. as a whole, and had no bearing on Alaska earning statehood which did not happen until 1959.
The California strike at Sutters Mill occurred when California was still part of Mexico. As late as 1846, two years before the gold strike, only 8,000 Americans were living in California, less than 10% of the area's total population. The vast majority (8000-12,000) were Hispanic. Most Americans who travelled west settled in Oregon territory. With the discovery of Gold at Sutters Mill on January 24, 1848, the flood gates were opened, and the largest migration the U.S. had seen to date erupted with many Americans, mostly single young men, moving to California. U.S. possession of California soon became an important issue for James K. Polk who ran for President on a campaign of Manifest Destiny. As President, Polk offered to buy California from Mexico, but the offer was refused. U.S. possession of California was an integral part of U.S. war aims in the Mexican-American War of 1848. The Treaty of Guadalupe-Hidalgo gave the U.S. possession of California.
No such political or social/economic upheaval occurred as a result of the Alaska gold rush. Although the answer above notes California's importance in the Compromise of 1850, the far more important issue was U.S. possession of California because of the large numbers of Americans moving there.
For the United States, the California Gold Rush of 1849 was much more important than the gold rush in Alaska in the 1890s. The major reason for this is that the gold areas of California were so much more accessible and so much nearer to areas that were easily settled. The gold fields of California attracted huge numbers of people to the area. Many of these people settled there because gold was not the only good reason for settling in California. So many settled there that California was soon a state.
This was important in the short run because it helped lead to the Compromise of 1850 and the Civil War. It was important in the long run because it led to the rapid settlement of California, which became a huge economic engine for the US. By contrast, the impact of the Alaska gold rush was much smaller on people who did not live in that specific area.