Ok, here's why things feel "samey" to some.
You roll up a first level fighter. You pick out 2 at-wills, 1 encounter power, and 1 daily. You note down a couple of class specific abilities, choose 4 skills from your class list, buy a weapon and some armor, and fiddle with the math until you have a first level fighter, ready to go.
Your fighter suffers a terrible fate brought on by Irontooth. Time to roll up a new PC. "Screw tanking" you think, I'm gonna play a wizard.
So you roll up a first level wizard. You pick out 2 at-wills, 1 encounter power, and 2 dailies (of which you can only have one at a time). You note down a couple of class specific abilities, choose 4 skills from your class list, buy an implement and cloth armor, and fiddle with the math until you have a first level wizard, ready to go.
See what just happened? The steps feel EXACTLY the same. Sure, your powers have different parameters (1[W]+Str vs. 1d6+Int), your weapons and armor is different, and your class abilities are different to fit your role, but in the end, both classes are the same skeleton with different clothes thrown on them.
The feeling gets worse as you level up. No class has new exclusive class abilities to look forward to; just another encounter or daily power at the EXACT same level as everyone else. In 3e (and earlier) classes gained unique powers at different levels (rogues get evasion at 2nd, rangers at 9th) or spells were different levels depending on class (Animate Dead: 5th level MU, 3rd level Cleric). Now? You get rituals at the same level no matter if your a wizard, cleric, warlock, or a fighter with Ritual Caster.
When all you have staring down the pipeline are more/better attack powers and a 1/2-dozen utility powers (most of which are just combat abilities minus the attack roll) The classes seem to blur. Who cares if the daily power you got was Fireball or Flame Strike; they're both Atk vs. reflex cubes that deal Xd6 + stat amount of fire.
It also doesn't help that every class gets better at fighting, casting magic, skill-use, AC and defenses at the EXACT SAME 1/2 level rate. Sure, it makes for easier math, but before the fighter had the best to-hit, the rogue had the best reflex save (by miles, not by +2) etc.
"But Remathilis." you say, "What about roles? Clearly a fighter doesn't share the same role as the wizard, ergo he doesn't share the same play-experience?" True, to an extent. Sure D&D has four roles (and they've always had them, more or less) but while a wizard might be in the back rolling to hit with magic missile and a fighter up front rolling to hit with tide of iron, another lingering element bubbles up:
Each role feels exactly the same. All defenders have a mark. Each mark might do a different effect, but at the end of the day it doesn't matter if your a swordmage, warden, or fighter, your main purpose is to run-up, attack, mark, and repeat. Same with leaders: Every leader has a XXX Word-like power that, as a minor action, gives healing surge + extra hp back. The individual amounts and methods vary, but sure as the sun is hot, if it says "leader" you'll find it has some variant on the Healing Word power in its class list.
Oddly, one role has avoided this straight-jacket: Strikers. Some deal Xd6 damage, some grant 2 or more ability score mods to damage, some just have insane [W]s to each power. A barbarian DOESN'T feel like a rogue because if D&D did anything, its created hundreds of permutations on ways to deal damage. Its also the reason controller doesn't feel unified; it lacks a strong-enough mechanical element (heal, tank, damage) to keep it unified. "Crowd Control" doesn't work well on its own.
Lastly, I originally thought getting rid of different "subsystems" would streamline the game and make it easier to play. Why learn a new mechanic just to play a wizard, psion, warlock, etc? Well, here's why. They played different so the game FELT different. A fighter could be a crafty tactician, or he could run up a kill-kill-kill. A wizard needed careful resource management and a more patient player (at least to be effective). A rogue needed to know the ins-and-outs of the skill system, etc. In essence, they were all little mini-games. Those mini-games are gone, and every class is poorer for them.
I think no one (except the most stubborn h4ter) would argue you could roll up a elf druid an play him EXACTLY as a dwarf fighter, but there is a lot of sameyness in the new "one class frame to rule them all" method of advancement. Classes like the psion (which eschews encounter powers for PPs) earlier would have fixed I think a number of complaints (for example, making wizards more daily-heavy while making fighters masters of encounter-powers).
Admittedly I did not get past page 3 in the how to remove homogeneity from 4E thread, so I don't know if this ever got picked up on. Also, I am a 4E fan who never understood what all this talk of homogeneity was about. But this post helped me understand far better, and several posts after by the "other side" helped me understand how folks where talking past each other.
I will highlight the first moment of clarity for me.
"You roll up a first level fighter. You pick out 2 at-wills, 1 encounter power, and 1 daily. You note down a couple of class specific abilities, choose 4 skills from your class list, buy a weapon and some armor, and fiddle with the math until you have a first level fighter, ready to go."
I read that, and thought, "THAT's an argument that 4E is homogeneous?!? Gosh! look at all the choices! I get to choose 2 out of 5 powers, 1 out of a different group of 8 or more powers, yet another 1 out of any more powers. I get 4 skills to choose from! I get at least 1 feat choice, a race choice with real mechanical relevance. Choices from many different weapons with their own stat choices and feat progressions! Compare that to a 3X fighter. If I'm lucky I get 3 feat choices, 3 skill choices, a much more diminished relevance for weapons, and a race choice that lets me get that 3rd feat."
As I continued to read Remathilis's great post it started to crystallize what this homogeneity was that he was talking about. He wasn't talking about the lack of variety of choices you get to make, but the lack of variety of the types of choices you get to make.
Later posts by "anti-homogeneity" folks helped me understand why this idea is hard to internalize. We all look and say, gosh, there are so many choices to make, that nothing feels the same. Some typical (but not actual) quotes.
"Each class plays differently"
"There are a huge variety of tactical choices"
"Obviously you have never played, as it plays differently"
"Each level has different choices to make"
While the "homogeneity" might say something along the lines of...
"Each class is built the same"
"Every round I am doing the same thing"
"Each class plays the same"
"Each level has the same choices to make"
"Each level has different choices to make" vs "Each level has the same choices to make" gets to the root of the talking past each other part.
An analogy. Say I am a carpenter. I love wood, different grains, species, color, warmth. I design and build a kitchen/dining room. I use cherry for the cabinets of the main part. I use maple for my island. I use a hard oak sealed for my countertops. I have a lovely chestnut brown bamboo for my flooring. I have a pine wainscoting that accepts a wonderful stain. I revel in the variety of my wood, working with each to interweave the grains together, making a wonderful composition.
Another person walks in and says, "Wow, that's a lot of wood! This kitchen could have used some color!"
One person revels in the details of what they are doing. In 4E they may love the tactical nature of combat, the battle for position. They like predetermining their powers, paragon paths and feats, trying best to align them together in a cohesive whole. They see the clear distinction between the 7th level encounter powers, and send considerable time deciding which best works, either from a tactical standpoint or thematically.
The other likes the "big" choices to matter. They want their wizard to do things differently, mechanically, from their fighter. They want the visceral around the table play experience to "feel" different. Roll different dice, use different rules, keep track of resources differently. They still revel in the different choices, but the choices they make are less concerned with detail, and more about the "big picture" idea they have in their head.
(of course insert a better description of the latter player in here, as I am clearly not one of them. I struggled mightily with that description.

I guess, looking back, 3.X clearly supported both kinds of player. There were certainly enough fiddly choices to made to satisfy detail guy. And there were enough mechanical differences that big picture guy was happy. 4E is probably more appealing to detail guy because he doesn't have to master many different systems to revel in the interweaving of complexity he likes. 4E is certainly less satisfying to big picture guy, cause there is only one system to dip into. One choice in comparison to all the myriad of choices detail guy sees.
Another way to put it. In 3.X you said, "I am playing a Fighter" and already choices had been made for you. You have an extra feat and no spells. That choice mattered. In 4E you say, "I am playing a Fighter" and you still have exactly the same choices ahead of you as if you were playing a wizard. You still have a class feature, the same number of at wills, encounter powers, etc... Your initial choice doesn't matter, in that you still have the same types of choices to make, even if your option for those choices are different.
At least that is what I have taken away from the discussion...