I personally don't understand the hate (strong word, but I couldn't think of anything else) towards class/level-based games.
Levels create awkward mechanics, like how a master alchemist/smith/flower decorator has to be able to withstand large amounts of damage in order to get their skill levels high enough to qualify as a master at their trade. And the corollary where being a master warrior lets you be a better carpenter/brewer/hair stylist than someone who has actually dedicated themselves to it. d20 tried to solve that by making non-adventuring classes like expert and commoner, but it didn't actually fix anything. They were still assumed to advance by gaining XP (the 3e DMG said so) more or less the same way as adventurers, even if it was in the background. There are these walls set up between what makes sense in the setting, and what the rules allow. It also, for me, has a psychological effect of implying characters with higher levels are more "important." Who wants to get into a love affair with a 0th level NPC, much less take them outside where a strong wind could kill them? The game treats them as a nobody. On the other hand, even if they are rather squishy, if those NPCs are better than any adventurer ever would be at their field(s) of expertise, and have interesting capabilities that have no bearing on combat prowess, the game has taken away that automatic assessment of their value as a character. Now the mechanics support a more nuanced and believable fiction.
Classes are less of a problem, but it's the same kind of problem. Being stuck in a class generally means you must have certain capabilities and cannot have others--even if that only manifests in what is harder or easier for you to train. Inevitably I find myself wanting to make a character with features from more than one class, but I can't do it well because the system doesn't have a class for that. Templates providing some pre-chosen packages are a much better system, because they give you everything a class does, but are optional.
Now, I'm not saying skill choice needs to (or even necessarily should be) a free for all pick whatever you want. There are plenty of ways to make it interesting. Maybe the better you get at one sort of thing, the worse you get at an opposed sort of thing. Or maybe certain types of skills are always found together (there are some things you really can't learn without learning others). But in order to reflect fiction, there need to be ways to represent characters with talents that break the mold.
You bring up a valid point about assessing the relative power of characters in a system without levels. Sometimes that's intentional because you aren't supposed to know, or it isn't really important. Honestly though, levels are usually actually worse in one area of that--they rarely give you a strong objective comparison. If you take a published D&D adventure, for instance, you often find NPCs that are given levels based on "how much of a challenge do we want this opponent to be for the PCs". So if it's a low level game, Such and Duzzle the Great is a 3rd level wizard, and in a high level game he's a 20th level wizard. If you look up a typical AD&D product that lists a bunch of NPC levels outside of context of adventures (setting material for instance), there is little apparent rhyme or reason. I think they were rolling dice to see what levels to set NPCs at (titles for levels in earlier editions notwithstanding). Apparently those levels mean nothing in the actual world. Now, I'm just talking about what I normally see here. There is no reason a level-based system can't have it's levels actually mean something (and whenever I run D&D I have to come up with such a frame of reference to avoid absurdity), they just usually don't (or barely do) in my experience.
Let's contrast that with a typical skill-based system (say oWoD), where the number of dots tells you how much training and accomplishment you are supposed to have in that skill. That tells me how I fit into a setting, not just how many ogres I can smack down. (Not that action resolution in oWoD actually worked out believably, but at least the concept of skill ranks was solid.) Just like not all level systems have the issue I mentioned, not all skill systems have the benefit I mentioned. Some of them just let you add more and more numbers without ever telling you what they mean. But the trend is for skill systems to do a better job here.
So, back to your point. If a system has a certain degree of complexity, and assessment of relative power in certain complex areas (like combat) is relevant, then a level-based system probably is going to have an easier time pulling that off. On the other hand, a skill-based (or to broaden it, I should say "non-level based" system, since there are alternatives to skill or level based) system might rank you in a certain category, and that might be all, or most, of what you need to know. A system with a "Fighting" and a "Thinking" stat, could tell you every thing you need to know to compare two characters in both of those areas with just those stats. "Fighting" is effectively your level for combat, and "Thinking" is your level for intellectual pursuits. Most systems are a bit more complex than that. Systems that want to tell you how good you are at combat (or some other general ranking) but aren't level based, could have a way to do so built in. To get back to one of my comments though, sometimes they actually don't want you thinking in those terms. Personally, I don't like stuck up design telling you how to play a particular system--make the system work very well a certain way, and more often than not that is the way people will want to play it. However, a decision to include or exclude such guidelines can subtly affect the mindset of players.
One thing I read years ago was the idea that a game really only needs a subsystem for something if that thing is going to be a focus of the game. Otherwise it can probably be handled by a general action resolution mechanic. So, for instance, if knowing how powerful your character is in a fight against others isn't an intended part of the game, there is no reason to have a level or other number or descriptor with that information, and having it there will tell people that it
is an intended part of the game.
In the case of oWoD there was little attempt to balance powers. Some types of supernaturals were just way stronger than other types, but the designers never intended the games to actually be played together (stuck up design there), so they didn't worry about it. I disagree with their decision, but at least it made it clear that you are supposed to be playing Vampire, or Werewolf, etc, and if you need a ghost and aren't playing Wraith, then you just use the rules at the back of whichever game you are playing and call it good enough. The games are theoretically in the same universe, but you aren't allowed to play them like they are (that's probably a good way of describing what irritates me about it).
Hmm. That brings up a point right there. Levels allow for a more objective measurement of relative power, which is primarily a game consideration. I don't think role-playing games are actually (intrinsically) games at all. I think they
can be games. I think they
often include games. I definitely think you
play with them. But I don't think they are always properly categorized as games. That's an aside, and I haven't written up my article on it yet, so I'll move on.
So putting that together, levels as a measurement of relative power, rather than as a unified or simplified (though ironically enough, level based systems are often more complex than non-level based systems) character advancement system, tell the player that relative power of characters is an important thing for this system, and signals that this role-playing system is intended to be a game. It also tells players that getting more of these levels is an important part of the game.
Most systems that don't have those sorts of measures don't want to give that message. So maybe levels are a good design choice for systems that focus on the game aspect. I'll have to give that more thought.