Their lousy nuclear technology and brassboard engineering resulted in warheads so heavy they had to build huge rockets to toss them over the horizon. This gave them a lot of lift power for putting something in orbit (there isn't much delta-V difference in hitting orbit from central Russia than there is in hitting a missile base in the middle of the U.S.)

Gagarin's Vostok spacecraft topped out at about 10,400 lbs. The rocket that launched it, a derivative of a Soviet ICBM, had a liftoff thrust of almost 900,000 lbs. The orbital Mercury weighed like 3,000 lbs, and was launched by an Atlas D (another reworked ICBM) with a liftoff thrust of about 370,000 lbs.

Unable to build large rocket engines at first, Soviet launchers often had huge numbers of smaller engines clustered at the base. Their proposed Moon launcher was a forest of engines at the base, and pretty big engines at that.

The Vostok spacecraft apparently was not capable of landing safely on land (a more difficult task than water landings), and Gagarin ejected and landed with his own parachute. The Soviets denied this for a long time, since technically it did not meet the FAI requirements for a successful spaceflight.

Once the U.S. got going, they pretty much left the Soviets in the dust. That the Soviet Shuttle was almost a complete aerodynamic copy of ours was pretty obvious.

Too bad, actually, since their basic design concept--a huge booster (intended for at least partial recovery) carrying either a largely propulsion-free orbiter or an immense cargo pod--was IMO somewhat superior to ours. It would have taken a lot more work to get a cargo carrier out of the Shuttle stack.