Weight will be about the same between two like campers since one requires equipment to lift the roof and the other has hard walls holding the roof up.
Center of gravity will be a little higher on a hard wall camper. If you pack heavy items up high, that CG difference will be more pronounced.
Since this rig be will dedicated to carrying a camper, consider getting a DRW truck. It will be as wide the camper, so overall width will be the same but the rear track will be wider even though the wheels sit under the camper wings. Typically you need to up fit any truck to handle a truck camper - Starting with a DRW, will require less additions and modifications.
Overall height will be a the biggest determining factor where you can go off road or in some cases rural roads. A hard side camper will typically be over 10' tall when loaded on the truck, so low branches and bridges need to be observed as well tight areas where the truck may lean to one side contacting a rock wall or tree at the highest point.
Cirrus uses the heating system you desire in their hard side camper. I am not aware of others, but someone else may chime in.
With upper cabinets and possibly basement storage, you will find there is more space to pack things in a hard side. If you choose a hard side with slide, some of that storage is sacrificed for ability to have more living space.
