My EE friends typically did more 'math' on a day to day basis, which usually amounted to setting up a set of equations for a different case of a problem that had been solved millions of times before in pretty much the same way.
My EE friends have gotten into big trouble when they tried to apply their usual problem solving techniques to ME-type problems without understanding the limitations of existing solutions.
Example: beam theory gives very inaccurate answers for large deflections because the classical equations were derived using small-angle approximations.
Example: fluid flow analogies are often used when teaching basic DC electricity, but real fluid resistances are square-law devices, and electrons don't freeze, boil, or cavitate.
On the few occasions when an ME has to resort to math instead of a hammer, the math can be pretty tough.
As Greg said, computers have changed that some, but there are still an infinite number of ways to inadvertently induce a computer to lie to you.
... and no matter which degree you get, you'll probably end up doing something from another specialty, or something that hasn't even been invented yet, so focus on optimizing your learning process, because you've only just begun.
Mike Halloran
Pembroke Pines, FL, USA