Hidden Hills is mostly all single-family homes, whereas in Calabasas gate communities, sometimes they look like homes, but are technically condominiums.
Hidden Hills community is entirely gated, meaning you need to enter through the security gate just to get into the area of Hidden Hills.
Calabasas on the other hand has certain subdivisions that are gated.
As for price, I would say they are similar. It just depends on what area of Calabasas you are looking in. Hidden Hills actually has a lot of homes for sale right now at almost $600/ square foot, whereas Calabasas is closer to $400-500/sq ft.