Whether it's alts in EQ2 or PTR characters in WoW, I've been trying out a relatively wide variety of different classes of late. There is a common thread between the two games in that both are currently designed with the goal that every class can solo.
EQ2: Root and Nuke
Looking specifically at classes that solo by casting spells, EQ2 accomplishes this goal by giving each of the casters a core skillset, consisting of a few nuke spells, a root, and some variety of buffs/utility. Beyond that, the majority of each caster's skillset gets rounded out with its niche role in mind; pure-DPS sorcerers get a larger selection of spells (needed for full DPS potential because all of those spells have cooldowns), Enchanters get buffs, CC, and debuffs, Summoners get pets, and the caster Healing classes generally have more durability (better armor plus the ability to heal).
You might expect the Sorcerers to be the best at the root and nuke playstyle, but it turns out that their longer group rotations can't be unleashed on solo mobs because the crucial root spell has a chance to break on any attack; your best bet is to hit the enemy with your 1-2 strongest hits and re-root, while the other casters can do things that won't risk breaking the root with that downtime.
WoW: Just Nuke It
By contrast, WoW has tuned its solo content such that everyone can burst down solo mobs in 3-4 casts. In practice, a pure squishy caster (Fire or Arcane Mage, Destro Lock) kills the mob in 2-3 hits, while a more control based caster (Frost Mage, Balance Druid) takes longer at less risk.
Because everything dies so quickly, many of WoW's casters do not get anything as good as a ranged root. They can afford to take the hits on the chin from an un-rooted mob because the fights are comparatively shorter. If the mobs ever get tougher, the solo advantage will swing in favor of the more hybrid classes in a big way.
(Aside: WoW's comparatively simpler rotations do have the advantage of making it easier to have diversity between specs of a class; you couldn't build something like WoW's Druid, capable of playing as a tank, healer, melee DPS, or caster DPS depending on spec, into a single EQ2 class, because you wouldn't have enough spells to support all of those roles.)
Building From The Core
In some ways, it is a bit disappointing to dig more closely at these systems and discover that you can have tons of classes (9 caster-soloers in EQ2) or specs (9 caster-soloers in WoW, if you don't count LOL-smite priests). Then again, such is the constraint that you have to build around when you have a primarily solo-based leveling game and don't want to end up with no support classes at your level cap.
None of which is to say that all of these classes are identical; in many cases, they play very differently. It just seems like the differences really come out with specialized group roles, where soloing basically boils down to DPS, control, and mitigation/healing.