Any class can do any of the solo content, and honestly the party content once fully geared up is probably mostly doable by all, maybe even better done by more support oriented classes if you are judging what can be accomplished.
Solo efficiency means things like, grinding exp while solo. This definitely is faster on some than others. I view it as just the characteristics of the class. Honestly mages blow everyone away at this, but when looking at who might be slower at it than others; a pure support healer for example, i can only approve of it. I was a healer for the first 5 years of my mmo career, and this was in games where being a healer really made you absolutely dependent on others. But what did this do? It made fewer people want to play the class, meaning i had an easier time grouping. More things like this to give different experiences of play between classes is a good thing. Likewise more dime a dozen classess people flocked to due to their ease had to put in effort in other ways to be attractive and successful overall. In the end both ways have shortcomings and advantages. This worked best when you really had to pick your class and identify with it, the class you picked was your entire playstyle of the game. These days everyone seems to want to just level up every class with lots of alts and have a bland similar experience, with only difference being the sequence of buttons they push while doing it, or the stats on the gear they look for.
However, this is more to do with class than advanced class. It might interest you to know that from what ive gained from the korean forums, they consider the stat bonuses you get for leveling up the advanced classes to generally be a more significant thing than the class unique skills you get.
Anyway, this depends on which class you are looking to play. A dps for example is really just going to chase the stat bonuses anyway, because even the advanced classes that theoretically give better skills for soloing will probably not in the end have the better stats for it. For the tank and healer this changes of course, where you must now not choose between multiple options of different kinds of dps, but rather dps or something else.
It should be noted that one might decide to just start with the best soloing class, farm the exp to max out the other two on that class, then end at the fully maxed out support build, and not have to worry about exp farming anymore. As the advanced classes, their switching to and leveling up of, is bought with exp you have banked in your general exp pool, and so you could very well grind enough exp to 5 star all 3 while sticking to a single one, or even do the thing some koreans recommend, which is to start with your favored class, and grind enough exp on it to max out the other two AND return to 5 star of the one you started with.
People do tend to group up for the dailies and weeklies anyway.