Yes, Capitalism does a better job at reducing poverty, provided you have already paid for the education and car and other means of being upwardly mobile. Socialism doesn't really ensure that people will be lifted out of poverty, but ensures that many people will have the same (awful) roof over their heads.
In theory, socialism makes everything equal. It provides the same income and economic status for everyone. If you are going to have the same lifestyle regardless of what you do, why would anyone ever want to work? Capitalism provides incentive to make money. Knowing that working harder and working smarter can provide a better lifestyle encourages many to do so.
In a capitalistic society the system is made to have poverty while socialism makes sure all basic needs are met while still providing incentive for work. Therefore, it would be easier to get out if poverty if citizens aren't concerned about having to meet basic needs. Socialism is not communism and is more of halfway between communism and capitalism. Most western societies have become socialist after the failure of capitalism in 1929.
In my opinion, socialism is the better economic system overall. For reducing poverty it's very clear that socialism does that better than capitalism. This has been seen in Venezuela (which, in my opinion, is the best example of a socialist country currently) after it became a socialist country in 1998. Extreme poverty was reduced by significantly by over seventy percent and general poverty by over half. Traditional socialism is NOT, "from each according to his ability, to each according his need", that is Marxism. Socialism is, however, "from each according to his ability, to each according to his contribution." In socialism, people do not lose incentive to work. As seen in Venezuela where unemployment was also reduced by over half since 1998.