Depends on how you count. The US had more astronauts killed in their space program while the Soviets had some rocket explosions that killed a lot of ground crew.
It's unclear if the Nedelin catastrophe should count. That was done by the military rocket program and not the Soviet Space Program. It did take place at the Baikonur Cosmodrome which is the same place the civilian space program launched it's rockets from. If you include the Nedelin disaster then you have to include the non-NASA/military rocket disasters of the US. I know the US had at least 2 ICBM disasters with heavy loss of life.
Plesetsk counts because for some reason everybody decided that launching spy satellites is the job of the civilian spaceflight programs.
Yeah, it was three cosmonauts during the Soyuz 11 mission. A valve broke open right before re-entry. The cosmonauts probably asphyxiated within 40 seconds. This all happened just above the Karman line (100km) which is what defines where space starts. The capsule finished the re-entry and landing process and they were found dead, they were still warm when the recovery team found them. After this the Soviets redesigned the Soyuz capsule, reducing the capacity to 2 people but allowing them to wear their spacesuits during re-entry and take-off.