I don't think any of the characters themselves have any weaknesses per se. They all just have certain advantages and lack the advantages of the other two, putting the player at a disadvantage in situations where he might need them.
It also seems like all three characters can fit the three archetypes (tank/support/dd) to some degree, although some are better at certain roles than others.
I think the advantages or roles can be roughly put like this:
I think his major role as support (specifically in higher levels) wills be that of a tank. He can wear shields and even has "Taunt", a tank signature spell in most games, to keep enemies off of you, and can stun, slow down, and intercept enemies when they're attacking you.
She is what I would consider something like "buffer" and classical "support" that you see in other games. She has spells to crowd-control enemies, keeping some of them from hurting you (she can hex a number of them, disorient a group and charm one to fight by your side).
He seems to be more like a classical DD support, perhaps to assist tanky characters that don't do tons of damage for themselves. He has CC abilities too, but these seem to be mostly to his benefit (he can blind enemies in front of him which is of course only useful for mobs that attack him already, and he can slow them down which will mostly help you to catch enemies who are running away). In addition to that, most of his abilities seem focused on increasing his own damage.
It has to be noted that all of them posses, at their highest skill level, some form of aura or buff for you and your follower that increases some stats. Therefor it would probably be wise to take these into consideration when picking a follower at higher levels:
The enchantress provides a 3% speed increase buff.
The scoundrel provides a 3% increase in your critical strike chance.
The Templar has class specific buffs which increase resource generation:
- 2 Mana regenerated per second for Witch Doctors
- 0.5 Arcane Power per second for Wizards
- 1 Hatred for Deamon Hunters
- 8% of all Fury generation increased for Barbarians
- 12% of all Spirit generation increased for Monks
Choosing one of these buffs is then a matter of your class, and skill build.
I also need to mention that in higher difficulties other attributes, such as health and dodge, probably play a larger role not only for the Templar (like one might assume since he seems tanky), but also for the Scoundrel and the Enchantress.
The monsters on those difficulties hit very hard. Often enough it will be very difficult to keep yourself alive, which means that it will usually look much more grim for your followers. Since my personal guess is that the focus of use for followers in higher difficulties will be their crowd-controlling abilities, since they most likely won't be able to keep up in damage, having them survive for a longer time (thus giving them a lot of Vitality gear) will probably become pretty important.
Finally: Which follower should you choose for your class? Needless to say, this will depend on your playstyle. A barbarian that is very focused on dealing maximum damage, and who doesn't use any of his life regenerating abilities or who only has few Vitality points on his gear, might make good use of a tanky Templar. In the same way, a tanky Barbarian might get much more out of damage-centric Scoundrel builds.
It's also possible that the buffs, later in the game, will play fairly large rolls, since e.g. 3% more chance to do critical strikes can have tremendous consequences on overall damage when your Strength, Intelligence or Dexterty values (for the respective classes that need them) are very high already, although this will probably end up being theory-crafted a lot by hardcore endgame-players.
However, I think it's indeed possible to look at what you're character is doing all the time and determine a smart choice for your follower. I would personally do it like this:
- Do you deal lots of damage and have no life? Tanky Templar
- Do you take lots of damage and have a high amount of life points, but only do medium amounts of damage? Damage Scoundrel
- Are you good, but not amazing at both? Crowd-Control Enchantress.
These are only personal suggestions however. One thing that Blizzard has, in my opinion, done very well in this game is to make a variety of different builds and setups very viable even in higher difficulties.