In fact you can find even more shapes of stringers at other manufacturers like Lockheed, Dornier, Saab, de Havilland or Douglas : U-shape, I-shape T-shape, H-Shape, C-Shape and Hat sections. There are quite different pros and cons for each design.
Aspects for choosing the one or the other design are :
- Accesability for automatic riveting by robots
- Buckling resistance to allow the actual frame spacing
- Corrosion prevention by not allowing water to be trapped in the cavity between skin and stringers
- Frame-stringer-intersection design, need of having plane flanges to attach clips or cleats to the stringers
- Placing the area center of the stringer in the plane of the rivet line perpendiular to the fuselage skin (to prevent the stringers from twisting if the fuselage is pressurized which might lead to cracks in the sealing and therefor corrosion problems)
- Repair provisions, can a doubler be added without problems ?
- Inspectability for cracks
It´s hard to explain about all this stuff without making sketches or drawings