how do capitalism and socialism compare in economic inequality?

There's a line in an album by the Firesign Theater: "That device is so powerful, it can only be used for good or evil!"

Capitalism and socialism are just different ways of running an economy, different sets of ground rules.  They could both be used to create a prosperous society where everyone is happy, well-educated, prosperous, OR a prison where a handful of people mysteriously become super-wealthy and everyone else is near starvation.

Any system can work or not work.  It depends on the people running the system--their competence and diligence, their goals and objectives.  Evil people in charge, evil system.  I have to say capitalism under the last few presidents has not worked especially well for most people.  The problem is not with capitalism itself, it's how we do capitalism.

Why is income inequality bad? Why should there be a limit on what you can earn? There will always be people that will only do what they have to so that they can just survive.

they can't hold a candle to Democratic Capitalism

In a socialist nation, there is one fat, well nourished person, and everyone else is starving. In a capitalist nation, obesity and nourishment are common. See if you can figure out the answer to your question

Capitalism promotes opportunity and freedom. Socialism promotes dependency and handouts.

Both are the extremes of evil. There needs to be some balance, which will be never. But capitalism keeps things flowing whereas socialism does not and makes for a co-depedant, socio-economic system.

Socialism helps EVERYONE while capitalism only focuses on the top.