OK so ill have a go at explaining!
Unibody vehicles are generally lighter, more structurally complex, and quite strong in impacts for the weight, as the chassis and body are sort of one in the same. There are different styles of unibody, with some bigger vehicles incorporating sudo-ladder frames into the bottom of the body, but they are always one in the same. In this category you'll find:
Passenger cars (last 70 years give or take)
most new SUVs
Body on frame vehicles are an older design, more mechanically simple, and often heavier. Almost all the structural strength of the vehicle is in the frame itself, leaving the body to be something that just needs to sit on top and provide a cabin, and rollover protection. This category includes:
95% of Pickup trucks
Most Commercial vans
The Arguments for Body on Frame design in off road vehicles are numerous, but the main ones include simplicity, strength, robustness and versatility.
Ladder chassis are all pretty much the same. 2 lengths of (either box section or C section) steel, linked with numerous crossmembers. Off of this structure are attached all other parts of the vehicle; the body on top via mounts, the axles below via the suspension components, the engine, the bumpers at the front and rear, and auxiliary stuff like fuel tanks and what not. If your looking to replace or repair something, all these parts are very easily visible and very easy to get to.
In a Unibody vehicle, these components are bolted to the "tub" itself, and depending on the shape of the vehicle, often require inventive ways of attachment and thus can difficult to access.
As stated above, Ladder chassis are steel. They're rigid frames propelled along with a body on top! This means when towing or hauling weight, all the stress is taken by the chassis. its very easy to build in strength, you just make it beefier. Think about the huge container hauling Trucks you see, all the weight is bearing down on those F*ck-off frames. In an off-roader, this means we can add weight to the vehicle and tow heavy loads (even reinforce the frame if need be), without worrying about the structure of the whole vehicle. In a Unibody this isn't the case, and the WHOLE vehicle has to be taking the strain.
Carrying on from above, Body on frame vehicles can take more punishment. Bumpers are attached to the frame not the body, meaning in small impacts, the force is directed down the strongest part of the vehicle, and not through the entire structure of the car. Also, although the chassis are rigid, theres always a degree of flex between the body and frame, meaning corrugations and impacts to the frame are somewhat isolated from the body. An impact for instance could damage the body badly, but could leave the frame intact, meaning you would be able to drive back to civilisation. In pickups this also means the tub can be isolated from the body, meaning heavy loads wont be twisting the body structure. In a Unibody construction whatever happens to the vehicle will affect it in its entirety, meaning higher repair bills, and less chance of scavenging a wreck. Unibody Pickups have to engineer loads of strength into the cab to haul the same weight as BOF ones, and often just choose to drop the towing/payload figures.
This is a biggy. when you develop a body on frame vehicle, you start with the frame, as all else works off it. Once you have this basic frame design, you can easily alter it to create variations on the same platform without having to completely start from scratch. Want a longer wheelbase version? no problem, stretch the frame and make a bigger body. Want a Ute? no problem cut the body in half and bolt a tray to the frame. Want a mobile elevated work platform (cherry picker)? no problem, bolt one onto the frame. You see where I'm going with this, anything is possible, not just from OEMs and skilled workshops, but average joes can customise BOF vehicles in their garage (I shortened the tipper back on my work Sprinter and bolted a toolbox to the frame). Winches and other hardware are easier to mount to a frame than a unibody, as are aftermarket bumpers.
With a unibody vehicle none of this is possible without SERIOUS re-engineering, as you're affecting the structural integrity of the vehicle. Wondered why theres no New Defender pickup yet? its because Land Rover has to completely redesign the monocoque tub to create it, and that's a hugely expensive process.
So all in all, for off road utility vehicles, body on frame is the way to go. They won't handle on the road like a unibody, they will no doubt weigh more, but at the end of the day, we're in the market for a Grenadier, not a Lotus Elise! The reason the market has swayed towards Unibody, is that none of these factors matter to the average person anymore. People favour Comfort, handling, economy (from weight savings) and price. Why build vehicles that are Bush proof when they're just going to the shops and back. Unibody construction offers a far more car like experience, and that's what sells to the masses.
I'm sure I've missed a few bits, and feel free no challenge some of my points, but I hope that's of some help!