Writing large systems of equations will take time. If big problems were easy, they would be called small problems, and you would be working on something more interesting.
If you cannot determine if your system is stiff, the ODE solver will tell you, in the sense that ODE45 will probably give up trying to solve it, trying to reduce the time step to a too tiny value. This is the simple test. It usually works quite nicely. If ODE45 does fail, then try a stiff solver. If the stiff solver worked when ODE45 failed, then you have your answer.
From your description, I'd not be amazed if the system was stiff. But stiff essentially means that you have some processes that operate MUCH more quickly than some others in your system, so they have seriously different rates. The ODE45 test is simple to try though.
