Why does your school offer an honors precalc II/Calc track for students after honors pre-calc/trig? Normally, you should be ready to start Calc.
If you are not concerned about testing out of Calc I or Calc I and II in college then I'd go for the HS class with the best teacher. At our local HS the honors teachers are often better than the AP teachers. What matters is that by the end of college you have a full understanding of all the math concepts needed to be an engineer (probably including Calc I, II, III, differential equations, linear algebra). It really doesn't matter when you take the math.