In my experience, neutering does not change a thing. A dog driven to work will work regardless of whether it has testicles or not. A bitch can have behaviour changes when due in season.
Neutering reduces the risks of prostate and ovarian tumours, infections and cysts, and mammary tumours in bitches.
An overweight dog is an overfed dog. Adjust there feed accordingly, yes they need less feed but we can control how much they eat to keep them slim

Unless you are seriously considering breeding then please neuter.