I think you need spend an hour or two looking at Functionalism and Marxism again. I cannot go through everything here but as the question states they are polar opposites. Functionalism asks the question 'what is it that unites us?' whereas Marxism starts with the thinking 'all societies have class conflict'. The Functionalists would move on to norms and values and how/where we learn them, these are the things that make us co-operate and function as a society (the biological/organic comparison).
The question asks what are the things that are similar and what is different? Both look at bigger things in society usually rather than smaller interactions and both would consider things are often determined for us (grand theory). Both have been considered more important than they are today, but Marxism probably still holds more sway. Marxism was a theory pretty much starting with differences caused by property ownership. Marx had a theory and not much research, whereas Durkheim tried to research things like suicide to show societies were not all the same.
Some often used failings of Marxism are that the world did not become communist and some thought class based issues had died (pakulski), or at least become less important. I don't think that is true and the world, indeed Britain is a very unequal society. Many people are now owners of companies, albeit through shares but does that give them any more power? No.
Functionalists thought all parts of society work together to produce a sense of harmony. When there are some functions not working so well, problems occur and society becomes disordered. Some disorder is good because it is a chance for society to adapt to change and introduce new systems. However, are we united as a society? Crime and disorder are still present, as is inequality.
Just some very small thoughts for you as a starting point.
theconsensustutor (WWW)