Which is taller?

Quick answer.. yes, flatbed will be taller.

We're 12'8"..

Possible to make it same? sure, but the structure of a flatbed is inherently different because of the assumed use, and, as pointed out, a 'bed' gains overall strength through the quarter panels (think unibody).
Different beasts.

I'd never go back.

JIMNLIN wrote:
Fleet Ford specs shows F450 pickup shows 38.3" ground to open tailgate with a small 9900 rawr.

Same specs shows the F450 cab/chassis 34.8" ground to top of the frame rails with a much larger 13660 rawr.
Specs does say these dimension may vary a bit with options

You will have to look at each upfitters bed assy to figure any differences.

Open tailgate should be roughly the same as the bed where the camper bottom sits.

Frame Rails typically sit 6-8" below the top of the rear tires and must be built up such that the bottom of the flatbed sits far enough above the rear tires that the tires do not contact the flatbed when the suspension flexes.

With a tall TC or roof air and a tall TC, You might be pushing 13'6". Me, I don't like looking up so I run a pop up on my 6 over stock 350.

And the COG moves up. Not what I'd want.

Regular bed is build with about 2" of raise since sides provide strength.
Flatbed with its own frame will add 6-8" to the height.

The specs probably don’t include the flatbed. That would make them about the same height. At least so close it worn’t matter much.

Fleet Ford specs shows F450 pickup shows 38.3" ground to open tailgate with a small 9900 rawr.

Same specs shows the F450 cab/chassis 34.8" ground to top of the frame rails with a much larger 13660 rawr.
Specs does say these dimension may vary a bit with options

You will have to look at each upfitters bed assy to figure any differences.

As mentioned below, flat bed is going to be taller than pickup box. Notice the air gap between the cab of my truck and the bottom of the camper. Clearance issues and side to side sway are the drawbacks I have experienced. It has it's pros and cons like anything else, but overall I don't regret it for my intended use.

Assuming the bottom surface of the flat bed 6-8" above the top edge of the tires...that will put the top of the flatbed higher than the floor of the pickup bed which sits typically a few inches below the top of the wheels (the wheel wells allow for suspension articulation).

I would expect the camper to sit 10-12" higher on a flatbed...assuming all else is equal (ie: you don't change the tire size or do a lift kit on the pickup bed option)