I would define 'best designed' as evoking the traditional story and flavor of the class Archetype very well with functional and/or elegant mechanics.
As such,
- I think Paladin stands high on that list, 5mwd complaints notwithstanding.
- Warlock might be awarded the most innovative design, but I think there are some interactions between the patrons and pact boons that are kind of wonky, as well as some invocations that less well designed.
- Fighter comes close, but MM's complaints about blandness are on target, and the Eldritch Knight seems to be lacking. Personally, I feel that the evocation school is a mistake; too little too late. As a fighter, the EK should be sticking the pointy end in the other guy for HP attrition, blasting kind of competes with that. Also, with the EK's slow spell advancement, by the time they get evocation spells the usefulness is doubtful. Abjuration and Transmutation are, IMHO, a better fit for enhancing the EK's fighting ability and keeping the theme of a warrior who uses magic to enhance and supplement his fighting ability.
- Cleric is solid, though more customization of abilities and spells through domain choice would be welcome.
- Wizard is very solid, just that some sub-classes don't hold up as well when compared to others.
- Rogue is also solid, just not as flashy as others. There may be some issues with Assassin, not sure.
- Monk is probably as good as it has ever been, with the blight of the Wo4E being the thing that takes it from the top of the list. To be fair, tWo4E sub-class is probably a more difficult and ambitious concept to incorporate into D&D.
- Sorcerer, has some problems, not the least of which is the lack of a clear mechanical focus & niche
- Bard, different than past iterations, but past iterations (with the possible exception of 4e and the pseudo-prestige class of 1e), were notoriously weak or lacking. Still not sure if it meets exceptions or story theme, but solid.
- Ranger, lacking focus, but with some bright spots. Probably trying to do too much with sub classes, perhaps needs a Hunter's Mark ability that is more like the Paladin's smite in implementation rather than a spell. Knowing all Ranger spells (once again, like a paladin) wouldn't hurt either. This isn't even getting into the whole spell-less/Pet identity issues.
- Druid. I like the idea of the traditional Druid class, but with a more flexible domain system on the cleric and spell list that is not as unique as it once was, combined with the Land Circle pilfering from the wizard list, it feels like a green wizard more than anything. Then there is the Moon Druid- interesting design, not sure about though.
- Barbarian. Okay design. Could see it as a sub-class of fighter. Totem Warrior goes further afield than the traditional 'berserker' theme, and may get into design space more preferable for a Druid/Shaman, but interesting nonetheless.