Having used both peeps and buckhorns-I'd have to say, both have advantages and disadvantages. First off, the key with the buckhorn is to use one you can see. If you have trouble finding the front sight, or seeing daylight around the post, then the buckhorn will simply not work. Assuming you don't have these issues then the buckhorn-for me-is the most accurate and the most easily adapted to elevation changes.
The peep sight is the most cumbersome to change for elevation, but assuming you shoot to your zero, and no farther, then the peep is by far the fastest to use.
I do find the aperture works on fewer focal planes than the buckhorn, but the aperture also limits the field of view.
If you have trouble seeing the buckhorn, an aperture can extend your enjoyment of iron sights for a few more years. When I could no longer see my buckhorn, changing to a peep allowed me to avoid having to mount an unwieldly scope. For how much longer, I dunno, but it worked for me. Hope this helps.