There is certainly something to be said for free enterprise. People having the freedom to build, create, and sell their creations has helped civilization advance. Monetary gain (and fame) is a huge motivator for innovation at the personal level.
I think that's undeniable.
But communists, fascists, and socialist states can create and invent, too.
There's just a different motivation. Instead of working for oneself for personal fame or fortune, one works for the government for national pride, job stability, or because you have no other choice. Whether we want to admit it or not, communist Russia and Nazi Germany created some great technological advances.
Ultimately, whatever the system, it's always the individuals (or groups of individuals) that create... whether it's in the private or public sector. Personally I think individuals are more productive when they produce for themselves and success lies squarely on their shoulders, but there's all types of motivations.
One of the advantages of capitalism is that it allows the individual to choose what he or she wishes to explore... the individual assumes the risk of failure, but if they succeed in creating something we all can use, we all win. On the other hand if taxpayer money goes to failed projects (or gets lost in the system), we have little to show for it. Of course certain projects (military, space, etc) are almost impossible without state involvement since it requires a huge amount of resources and tend to be very long term projects with sensitive information.