It's recently come to my attention that I cut peppers different to pretty much most of the population, using neither of the above methods.
I stick a knife in at the top by the edge of the green stem, and cut around the stem. Then make a vertical cut down one side of the pepper and up the other side.
Pull one side off the stem, then the other.
All the seeds stay on the core bit of it, there's virtually no wastage, and you've got 2 equal shaped pepper halves which are good for stuffing if you want a big surface area for cheese.