What made the Soviet Union such a big threat is that their military rivaled the US in terms of strength and technology. How could the Soviet Union keep up with the United States in military spending? Why can't China have a technologically advanced military like the Soviet Union? Is it because they don't spend enough money?

It is in good part because the Soviet Union had a much more ruthlessly millitary oriented economy whereas China does not. You have to remember that the U.S. and the USSR begin the cold war straight out of the starting gates of WW2. So both countires already had very very large and complex weapons programs and armies already constructed whereas everything about China was devestated durring WW2.

There is also the bullets vs. butter thing going on. USSR cared a lot A LOT about bullets whereas modern China is more focused on butter. Note that the chinese don't have to wait 6 years on a list to get a new car like the 80s Russians did.