The definition I follow, and what I think would be better than our current system and a laissez faire market system, would be a publicly planned economy. This would be an economy where the enterprises belong to the public as a whole, and the members of the public would therefore have social control over these enterprises' production and distribution. The members of the public would use this social control to democratically plan out the production and distribution of resources, either directly or indirectly through representatives, or both.
However, there are other definitions of socialism that I respect as well, such as social democracy and market socialism.
The problem with this kind of question is that it all depends on what your definition of socialism and capitalism is. Forms of capitalims such as anchor or laissez faire capitalism are absolutely terrible but so are the Marxist forms of socialism. In my opinion a market socialism is probably the best form.
I don't like that picture, I don't think the comparison of 'Competition vs. Cooperation' is an accurate one. Capitalism in reality and ideology uses both to gain success for its constituents.
Socialism as an idea seems good. But only as an idea. Not as a reality. It sounds great for all the imaginary people I can dream up following it in my head ... But then I realize those people don't really exist ... And the ones here can never make something like that work. So I protect myself from the ravages of them trying for socialism and failing by subscribing to capitalism ... Where anyone can win.
The free market is what has brought about the greatest developments in human history and protection of the free market must be a priority for any country that wishes to innovate and advance. Socialism, true socialism at least, cannot function as it eliminates the incentive to work hard and innovate since monetary compensation for exceptional ideas and hard work does not exist. Socialism is a system where the lazy and unintelligent are rewarded at the expense at the hard working and intelligent. The innovators pay for the slackers to live an easy life. I believe in opportunity to make something of myself and be as successful as I desire, with the only limitation on my own success being my own work ethic. While pure capitalism is destructive, a government that strongly favors Capitalism while including Socialistic elements where necessary is ideal for development, quality of life and innovation.