Why do typical acetylcholinesterase inhibitors (like carbamates) have a greater parasympathetic effect than a sympathetic effect?
We were taught that ganglionic receptors have very high thresholds. So we need a very high concentration of the drug to produce the sympathetic effects. We even solved a hypothetical problem in class, where a patient presented with a pinpoint pupil (typical insecticide poisoning) and increased secretions but an increased heart rate (usually they present with bradycardia). We would still treat the patient with atropine since the combo of pinpoint pupil and increased secretions would be exclusively explained by insecticide poisoning (either organophosphate or carbamate). The increased heart rate could be explained by ganglionic action leading to sympathetic activation of the heart. 

But as said this was only a hypothetical case and patients of organophosphate or carbamate poisoning always present with bradycardia. To elicit ganglionic responses the person has to consume a dose way higher which would certainly lead to sudden death.

Hope that helps :)