In 3rd Edition there were three progressions for your Base Attack Bonus (a value that was added to all attacks)and two for Saving Throw Progressions (you used to roll a save against a target DC, which is an inverse of the way 4th Edition does it).
4th Edition gives every class a blanket bonus of +1 for every two levels, regardless.
3rd Edition gave each class a list of skills that you could purchase bonuses in easily, and whatever else cost double for the same bonus. These skill bonuses could be augmented by race, feats, magic items, etc, but otherwise saw no increase unless you invested skill points into them.
4th Edition gives everyone a +1 bonus for every two levels, and a +5 if you are trained in the skill. Race, feat, and other stuff apply, but you never invested anything else after that: everything increases every other level at a constant pace.
Most often this statement is aimed specifically at powers. Attack powers follow the pattern of making an attack roll to determine success, and then letting you deal damage and/or some kind of effect if you hit. While each power might follow an identical pattern of roll-and-effect, there is more to it in the actual narrative of the game and style of powers.
In 3rd Edition, attacking came in two flavors: you either made an attack roll, or if you were a spellcaster you selected a creature(s) and it had to make a "defense" roll. Single roll, and the only variance was who had to roll it.
4th Edition made things more consistent by making it so that if you wanted to attack a creature, you make the roll, no matter how you are going about it whether by sword or spell. I like this kind of mechanical consistency because it also makes it a lot easier to generate rules to determine if your ability works or doesnt. In 3rd Edition the saves got pretty wonky, and since they were based on Hit Dice and type it could be very difficult to make a monster with saves that werent too high or low for its Challenge Rating. The designers are free to focus on one set of functioning mechanics and then just move on.
I contest that 3rd Edition was far more guilty of "samey attacks" than 4th Edition since classes followed the roll-and-damage pattern without any kind of variance. Barbarians, fighters, paladins, and rangers all did largely the same routine: make an attack roll, deal damage if you hit. Rangers didnt have the mobility they did now, barbarians did inferior damage to everyone else unless they were raging (they broke even with fighters due to Weapon Specialization), and paladins could call on their god for divine power once per day...if the target was also evil.
4th Edition adds context to powers so that even if on a pure mechanical analysis they perform similar or even identical functions, they wouldn't be described as such. That's a big deal for me: classes feel and play differently than they used to. As a rogue, I feel more nimble and agile than a fighter, even though we both like move right up to a monster and stab at it. As a wizard I don't feel like a sorcerer, who was actually virtually identical in every respect except for class features (which didn't amount to much).
To sum it up, I'll concede that in 4th Edition many things seem the same if you look at it from a purely mechanical standpoint. If you strip away the power sources, context, and narrative, you'll probably find that many things follow an identical routine. However, I would say that 3rd Edition is far more samey in that regard since so few things did anything more than just plain damage. I think that both games would be said to have samey things, but 4th Edition doesnt have nearly as many, and if you add in a bit of description then it becomes much more diverse than it already is.
In closing, if elements in 4th Edition are samey, then elements 3rd Edition are virtually identical to themselves.