Progression is still progression, regardless of what type it is, older character will always be more versatile / efficient than fresh character.
There isn't any sense in claiming otherwise.
The point of horizontal progression, though, is that power gap between old character and fresh character will not be as large as it would be in vertically progressed game.
No levels, equal base character stats, and limited skill slots in skill bar, will still give a full fresh character, chance against old character, because playing skill will play a significant role here.
In vertically progressed MMO, fresh character would not even have a chance regardless of playing skill.
Of course, we are talking about fresh characters here, not fresh players. Fresh players will obviously still have much to learn, so from that fact alone, they will be behind old players, that already learned many tricks.
However, if old, experienced player, creates a fresh alt, he may very well beat many other players (that are using progressed avatars) with his own freshly made alt, purely through his playing skills, and experience.
The above would not be possible in vertically progressed MMO.