When you say the "F Horn (alto)." Its actually an Eb Alto Horn, not in F. The Eb Alto Horn was used in a lot of american marching bands before 1950's (or early 1960's) before the mellophone took off. The Eb Alto horn is used in british style brass bands. Mellophones are by far the most stable of the horns. G bugles (for better or worse) have died out. Band programs won't use them, and the only people in the world that I know of that have used them is DCI years ago. Obvious there are some DCA and alumni corps probably using them. I've only heard bad things about a true Bb Horn. Now, I know there are some groups that use Flugelhorns as Bb Horns. Which can be okay when written right, and if you have a good flugel.
The mellophone (in F obviously) is IMO by far the best option for marching horns. Easily accessible for purchase (bc of its wide use), and a lot of quality made mellos are out there (Yamaha and King being the top two). The mellophone responds just like a trumpet. Similar pitch tendencies, same fingering system, the instrument has the same written power range as a trumpet (except most horn players can't hit a high C off the staff unless they are a true trumpet player which has moved over). The ONLY issue that comes of the F mello is that they are the odd ball pitched instrument on the horn line. Tuning to concert Bb can be difficult b.c. the low brass and trumpets are on open partials, while the mellos are using a first finger valve combo. Tuning to a concert F can be a good idea which some corps do b.c. that puts everyone on the line on an open note.