Just to add my $0.02:
Dielectric grease will provide a better contact (when compared to bare metal-to-metal contact,) as well as exclude both air and moisture, reducing or preventing corrosion buildup between the points of contacts.
I'm sure there are other reasons not to use petroleum jelly on the battery terminals, but my personal reason is temperature. It gets hot under the hood and petroleum jelly likes to run at even slightly elevated temperatures. Heck, it becomes pretty fluid even when applied to skin.
As far as I know, petroleum jelly provides similar corrosion inhibition and dielectric properties - maybe not as good as a dielectric, but I'd better the difference is of little consequence.