First, one must define what Marxism is. I bring this point up because Marxists may range from Democratic Socialist of America (whose idealogy could be almost defined as "Democrats who like Karl Marx" to quasi-fascist regimes of Stalin and Mao (whom many Marxists believe to be antithetical to both Marx and democracy). Marxism can also take the characheristics of worker council form (e.g. Industrial Workers of the World [IWW], Socialist Labor Party, etc).
Assuming you define Marxism as being "a society where everyone owns and shares property and the means of production," I would then compare Marxist democracy to Capitalist democracy.
In Capitalist democracy, two political parties (e.g, Republican & Democrat, or Tory and "Labour") are sponsored by corporations to enact policy on their behalf. Skeptical? Just ask any of your classmates the following hypothethical question:
"If you and an oil representative (banker, tobabbo lobbyist, ...) were trying to arrange a meeting with your representative, whom would the rep mostly likely see first?"
Or if one were to make up a list of bills passed that favor corporation versus legislature that favors workers, the list could revealing just how democratic Capitalist society is.
Income disparity: Can democracy function where 5% of society own over half of the wealth?
Can democracy flourish when Corporate candidates can outspend radical candidates 1000:1?(I'm guessing on ratio)
If you haven't already done so, I would encourage you to check out the Corporate Watch website, the Economic Justice website to name a few. Also perhaps browse the (Noam) Chomsky pages, as well as Howard Zinn and Michael Parenti.
Good luck and I hope I was of some help