IIRC Glenn's flight was less than an orbit, whereas Gagarin's was just over. The USA were mortified to be beaten into space with Sputnik and even more so when Gagarin flew. They launched Glenn on a sub-orbital flight in order to regain some lost national pride. Also Glenn had no control over his capsule. The US astronauts had to fight for flight controls in the Gemini (2 man) flights and the first design of the capsule didn't even have a window.
Other differences are:-
The USA practically invented the PC in order to get Apollo into space, the Russians used a chronometer powering a drum with a paper trace of a graph for there Soyuz.
Russian space craft were pressurised to 14psi and used air, the Americans used a much lower pressure and breathed pure oxygen, hence the Apollo fire on the ground in tests which killed the three crew.
Both approaches had their advantages but for me the fact that the only way to get into space for the next few years will be via the Soyuz shows which was best.