The class system of Skyrim is really no different than the class system in Oblivion or Morrowind.
Morrowind / Oblivion: You tag a specified number of skills for an early bonus, and leveling these skills levels your character. There is no game mechanic limiting to you to only these skills. You can still use any and all skills, whether they are one of your chosen skills or not. The class system is really nothing more than a label on your stat sheet telling you what you are, but really doesn't do anything in terms of gameplay. There is no real means of specialization, as if you play long enough, your character will begin to increase skills and attributes that aren't definitive of the character, just because you've maxed everything out. If you play long enough, in the long run, all characters become the same.
Skyrim: You don't tag any skills, thus you don't get an early bonus. All skills work towards leveling you up. You can still use and level any and all skills. The difference is that this time around, there's no arbitrary title on your stat sheet telling you that you are a "Warrior", "Mage", "Thief", "Battlemage", "Assassin", "Nightblade", "Spellsword", "Necromancer", etc. You just simply play as that.
You got it wrong, there is no "bonus" in Morrowind or Oblivion, you choose who you are. Let me put it this way: in Morrowind, if you choose a barbarian class, you're going to get a axe boost. BUT, if you choose a mage class, your axe skill with be below acceptable, you will miss most of your blows. Why? It's not because the barbarian got a bonus, it's because the barbarian didn't wield his first axe when you started the game. Your mage on the other hand, probably never touched an axe, so it's only normal he's going to be pretty bad at it and rarely manage to hit his enemy.
In Skyrim, you start the game and you are competent at EVERYTHING. You shouldn't be able to unlock chests so easily if you never touched a lockpit, you shouldn't be able to hit an enemy square in the head with a giant warhammer 10 times out of 10 if you're a feeble wood elf thief. The class system IS different. Morrowind forces you to play a specific character, while Skyrim enables you to do anything you want. Sure, someone who never touched a lockpit can get good at some point, but it will take a helluva lot of time to get started, to understand how it works. Unless you train until you are competent enough. In Skyrim, you are already competent. You're like a jack of all trades who chooses to specialize. And the moment you have a bit of an idea to of what you'll be, all the choices become obvious, so it's like you choose a class, but quite differently like I explained.
And you got attributes. In Morrowind, attributes add "bonuses" to your skills. Someone more intelligent will be better at alchemy, while someone with more speed will be better with daggers, and someone with more strength better with long blades. It's only logical. The harder you're going to strike with a long blade, the more damage you'll do, besides your skill with it. But it's more effective to strike faster with daggers. And each attribute govern several skills, that's where things go deeper. A jack of all trades will have harder time because he won't be able to focus on all attributes, but someone only focusing on strength and endurance skills will have a significant boost early on, and for most of the game.
So the real difference is perks, which actually creates more customization and specialization than Morrowind or Oblivion. In Morrowind or Oblivion, someone who was 100 in Conjuration was the same as everyone else who was 100 in Conjuration. In Skyrim, a level 100 Conjuration character can be specialized in Necromancy, and reanimating corpses to fight for them. They could be specialized in summoning Atronachs from the realm of Oblivion. They could specialize in Bound Weapons and harvesting souls with ethereal weaponry. They could even be completely unperked, and otherwise unefficient in the skill.
A level 100 Blade / Blunt (or Axe / Short Blade / Long Blade / Blunt Weapon in Morrowind) is the same as a 100 in the same skill. In Skyrim, a level 100 One Handed character could be specialized in Blades, Maces, or Axes. They can be specialized in one handed power attacks. They could be specialized in Dual Wielding and double weapon fighting.
I just don't understand the argument about the lack of classes in Skyrim. Classes literally did -nothing- in Morrowind or Oblivion. Skyrim is lacking only a label, but effectively, actually encourages classes much more than Morrowind or Oblivion ever could.
Perks are a good addition, but could use some work. Besides, they are not mutually exclusive to classes. Too many perks are sub-skills, making then no different than skills. One handed and two-handed skills are stupid. I can understand using claymores is different than daggers, but what about blades versus axes? The difference between war axes and battleaxes is basically a question of strength and endurance, while the difference between axes and blades (and long blades and daggers) is more important. Since there's less skills and there's not that much perks, some choices are too easy. Some perks necessitates others in order to be unlocked, and at a specific skill level, so usually after the first few levels, you don't even need to choose which ones to unlock anymore, as the others are locked to you for the moment. If you're going to be a barbarian using giant weapons and heavy armors, some perk choices will be obvious. Ie. you won't use perk points for shield perks in blocking when you only use claymores. And you're certainly not going to use perk points for alchemy. It didn't took long that my barbarian-type of character was already defined with the perks already chosen. I put points in smithing because otherwise I'd bank on perk points and I just needed to use them once every 20 levels or so.
Perks do add a bit of depth and complexity, but more than people give them credit for. It would work better with more skills and more perks, thus you can customize much more your characters. You know, I don't consider a warrior character much more different than another one because he can chop off heads or is good with war axes instead of battleaxes. There's perks offering more customization, but there aren't that much, again a certain number of them are actually skills rather than real perks. And I don't like the magic thing that certain spells require certain perks. Anyone studying the conjuration school should be able to use any spell. BUT, not everyone would be able to do detect life up to 1 kilometer, you know, anyone with he basics of illusion should be able to be invisible for 2 seconds. But then, a mage specializing in illusion will get all the perks anyway... Or someone using only certain spells from different schools with choose different perks, but how is this any different than a Morrowind mage who only use certain spells for each magic school?