Besides limits of cleaving riding is another thing to remember when riding mounts you can't use long bows or Arbalest (assumingly). Only short or composite bows and assumingly only with the riding proficiency. If everyone else is melee you will really want to pick up precise shooting to allow/remove the penalty to shooting into melee. If all you want to do is be a ranged fighter I would suggest Barbarian as you can get precise shooting to start with and lower that penalty by picking it again and you get more health on average.
They have a similar selection of proficiencies to choose from. So the real question if it is just down to the two of them is do you want more combat ability (More HP and Reroll mortal wounds) or out of combat ability (Hiding, Evading, and Navigation).
Last is presentation and ease of travel. An Arbalest and long bow are unwieldy but effective weapons. They weren’t made to hunt with so dropping one down on a bar table or just carrying it around unslung could be cause for trouble.