I love my flatbed. There's a lot more space, and it's easier to properly strap things down. The downside is, pretty much everything has to be strapped down unless you build some sides that drop down into the stake pockets.
You can side load with a forklift. In a regular pickup, you might fit two pallets in if you take the tailgate off, and use one pallet to push the other all the way to the front of the bed. Good luck getting that front one out, too. :laughing: I can fit 4 on a 9' long flatbed, and 6 on a 12'. Each one is easily forklift accessible, too. What you want to do sounds ideal for a flatbed.
I'd recommend you get rub/ strap rails down the sides, not just strap to the sides. Most pickup sized beds are 96" wide, and the extra couple of inches the rails stick out make it much easier to hook straps if you're loading pallets on it. Be sure when you start looking for beds you make sure to find ones made for a truck with a pickup bed. 'Regular' beds are designed for chassis cab trucks, and the frames are a little bit different. Neither one is really better, but it is something to be aware of when you're shopping.