Different people might see different similarities between these systems, depending on the exact definitions that they are using. I suggest that you consult your textbook and/or your class notes to see what answer your instructor expects to see.
In my view, a major similarity of these two systems is democracy. While democracy is not absolutely essential to either of these systems, it is the most common form of government in capitalist countries and even in socialist (as opposed to communist) countries.
With regards to economics, the main similarity between the two, as I see it, is some amount of market competition. A purely capitalist economy (no country has such an economy) would be run completely by market forces. The government would not intervene in the economy at all. A socialist system would be under more government control than a capitalist economy, but there would still be many market forces at work. People would be able to own private property and make many of their own economic decisions. Small-scale private enterprises would be allowed to exist. Thus, both systems would include market forces, though such forces would play a larger role in a capitalist system.
Democracy and market forces, then, are the main similarities between these two economic systems.