Question

Will current flow more easily through a thick wire or a thin wire of the same material when connected to the same material when connected to the same material, when connected to the same source? why?

Answer 1

For the same material and the same length, the thicker conductor always
has lower resistance.  That means that if the same potential difference exists
between its ends, then more current flows through the thicker one.

A good intuitive way to think about it like this:  Electrons have to move from
one end of the conductor to the other end.  If there are more paths available
for them to take, then they don't get so bunched up, and it's easier for them
to flow in the conductor.  Just like a highway for cars.  If there are a large number
of cars trying to drive from one end of the highway to the other end, then it'll be
a lot easier for all of them, and more of them will get through every hour, if the
highway has MORE LANES . . . that is, a THICKER road.

Answer 2

Its in thick wire cause the size of copper increases and more space is given there for current 
thats it :)