In a government with both president and prime minister, which of those two is more powerful?

There is no
one answer to this that is correct for all systems that have both a prime minister and a
president (or which have equivalent offices).  The relative amounts of power are decided by the
constitutions of the individual countries. 

To see how this is true, let us
look at the examples of France and Germany.  France has a system in which the president has the
most power.  The people that everyone sees as the leaders of France are the presidents.  Nicolas
Sarkosy was the President of France.  Right now Francois Hollande is the President.  These men
are known around the world.  By contrast, the Prime Minister is a man named Jean-Marc Ayrault. 
He is not well-known and generally has less power than Hollande does.  In Germany, however, the
Prime Minister (called the Chancellor) is much more powerful than the President.  Here, the
Chancellor, Angela Merkel, is the person known as Germanys leader.  The President is named
Joachim Gauck.  His responsibilities are mainly ceremonial. 

Thus, we can see
that there is no one answer that fits all.  Different countries have different
systems.

href="https://en.wikipedia.org/wiki/Politics_of_Germany">https://en.wikipedia.org/wiki/Politics_of_Germany