It's all about the thickness of the gel and not about the compounds to be loaded onto it. When running sequencing, the gel is vertical because it has to be thin for better resolution. When running classical agarose gel, horizontal position is OK for protein and DNA and resolution will be less. And also it wouldn't be easy to load a thin gel in the horizontal position.
As said by David, all has to deal with the relative mechanical strengths of teh gels, acrylamide gels are way more resistant to emchanical constrainsts than agarose gels.