This might be a question relating to all of eastern Russia, but I focused on the more clearly similar ones. Primorsky Krai is at 12/km2 while Heilongjiang is at 70/km2. Why couldn't Russia develop these regions like China could? Did they ever attempt to encourage migrants from Asia?
Looking at a topographic map will tell you part of the story, but not the whole story. Parts of Heilongjiang are flat, and some are mountainous, but the plains lead all the way to the sea, and are accessible from the rest of Eastern China, the population hub of the entire country. Even today, the Russian Far East is much, much, much harder to get to from Western Russia, where most of the people live. But still, there are cities there, and they exist for a reason, and it's a pretty interesting story.
By the end of the 18th century, Russia claimed sovereignty over territory extending from present-day Poland in the west to the Bering Strait in the east, and had established trading colonies in Alaska. However, in the eastern part of this vast periphery, imperial control was superficial at best, if not completely imaginary. As the historian Steven Marks described it, the eastern fringe of the Russian Empire was a “weak and distant domain.”
Western Siberia, just beyond the Urals, is relatively fertile and was settled by Russians quite early. In the east, there were the cities of Petropavlovsk and Yakutsk, which were accessible by water, but basically impossible to reach by land. Seriously, it's difficult to overstate just how hard it was to cross Eastern Siberia by land. You can follow steppes and valleys as far as Lake Baikal, but beyond that it's rugged mountains all the way to the Pacific. The Russian Empire sent Cossacks to the Far East in an attempt to subdue the small indigenous population and farm the land, but in such a forbidding environment it proved incredibly difficult to do both.
By the mid-19th century, China and Japan had opened to trade, and the California Gold Rush had shifted the gravity of the global economy to the Pacific Rim. Russia desperately wanted in. With the formal acquisition of the Amur region from China, the economic future of the Russian Empire was expected to take shape in the Far East, and integrating the region became a priority, especially since many Russian elites feared that a distinct settler mentality would take root in the "Wild East." The Trans-Siberian Railway was conceived as much as a political necessity as an economic one. Strong links between East and West would prevent separatist stirrings, and allow the flow of people, power, and products from Europe to the Pacific Rim.
Modern Helongjiang itself grew up largely as an extension of this project. After China lost the Amur region to Russia, Han Chinese were allowed to migrate en masse into the sparsely populated and Manchu-dominated borderlands. The mentality was the same--populate the region with the dominant ethnic group to reinforce the territorial integrity of the empire. But for Han Chinese, the journey was much shorter and easier than the journey from European Russia to Siberia, and arable land was much easier to come by. Quickly, Helongjiang became the breadbasket of East Asia, and became a major exporter of food to the rest of the region.
China's imperial neighbors, Russia and Japan, took note, and began to see Manchuria as quite lucrative. The modern city of Harbin grew up around a Russian-built railroad linking the Russian port of Vladivostok (the planned terminus of the Trans-Siberian Railway) with Beijing, and was originally built and populated mainly by Russians. Harbin was an incredibly cosmopolitan city, and functioned as a de facto Russian colony in Manchuria, even after Russia's defeat in the Russo-Japanese War led to the loss of its railroads and footholds in Southern Manchuria.
The Russian Revolution slowed Russia's commercial ambitions in the Far East, but a massive wave of Russian émigrés arrived in Harbin. After the Japanese conquest, Manchuria was aggressively industrialized. After World War II, Manchuria became the power center of the Chinese Communist Party, and was rewarded with attention from Beijing, which focused many early industrialization efforts on the region, due in part to its proximity to communist China's then-ally, the USSR. The bulk of Helongjiang's explosion in population took place during the postwar period of industrialization.
Basically, Russia tried in the 1800s and early 1900s to do what China came to do in Manchuria later on, but geography and a relative lack of arable land made the Russian Far East a pretty unattractive destination for migrants. The relative proximity of Helongjiang to major Han population centers made for easier access, and better land made it easier to settle down. But the biggest divergence happened in the 20th century. The most economically important Russian settlement in the region was Harbin, which was actually in China. But the biggest difference is that, for Russia, populating the region simply ceased to be a priority, whereas in China the political and industrial weight which had accrued in the region, largely as a result of decades of quite brutal colonization, made it an attractive destination for post-war internal migration.
SOURCES:
Steven Marks, Road To Power: The Trans-Siberian Railroad and the Colonization of Asian Russia (Ithaca: Cornell University Press, 1991).
Imperial Visions: Nationalist Imagination and Geographical Expansion in the Russian Far East 1840-1865 (Cambridge: Cambridge University Press, 1999).
Mariko Tamanoi, Crossed Histories: Manchuria in the Age of Empire (Honolulu: University of Hawai'i Press, 2005).
EDIT: Thanks for the silver :D