I prefer both, being an RPG enthusiast.
Depends on the gameplay and interface.
Games like Final Fantasy 1-whatever, for instance, are pretty amazing with their random encounters. They do throw some visible encounters in there though, so you can be prepared for a tough fight.
Games like Star Ocean: The Last Hope, the only kind of battle in that game were Visible Encounters. You could have avoided them all if you preferred, yet you would be at a disadvantage due to lack of experience.
Doesn't really matter to me at all. If the gameplay is good I couldn't care less what kind of encounters there are...