Your tests are not exactly equivalent. I think your teacher may have had something more like the following in mind:
def breakTest():
i = 0
while True:
i += 1
if i == 10:
break
def booleanTest():
i = 0
while i < 10:
i += 1
As you can see below, putting the condition into the while statement instead of having an if/break does improve performance (and shorten code):
In [14]: %timeit breakTest()
1000000 loops, best of 3: 999 ns per loop
In [15]: %timeit booleanTest()
1000000 loops, best of 3: 201 ns per loop
Note that this is just an example of the different ways to exit the loop and what I think your teacher meant. Of course if you were actually writing this code, you should use for i in range(11): ...