OK. Let's compare 4e to previous editions.
vs 2e - 2e skills are very minor modifiers to straight stat rolls unless you've chosen to take combat NWPs or NWPs like Bowyer/Fletcher. 4e skills are major modifiers to stat rolls. Meaning that training is almost more important than stat. It's a different emphasis but one that means that what you are trained in makes more difference so a broader range of archetypes is available. But it's close
vs 3.X.
3.X fighters get 2+Int skill points/level trainable out of the following list
4e Fighters have 3 skills trainable out of the following list:
Athletics (Str), Endurance (Con), Heal (Wis), Intimidate (Cha), Streetwise (Cha)
Doesn't look like much of a difference, does it? 2+Int out of seven vs 3 out of 5 (incidently the fighter has the worst skill list in both games).
But let's look at those skills for a second.
Climb, Jump, and Swim between them in 3.X all are
one skill in 4e. Athletics. So if you want to be very physically adept in 3.X (and let's face it, most fighters do) you need to borrow skill points from somewhere. You don't have to compromise on being superbly physically adept and still have two skills left over. So the archetypal 'Strong Guy' skills now take one pick not three - a huge advantage for the 4e fighter.
Ride's gone. Anyone's assumed to be able to stay on the back of a horse under basic conditions and to be pretty crummy in combat (which is all ride really gets you). If you want to be really good at riding you need the mounted combat feat in both editions, so spending skill ranks on it in addition in 3.X is annoying. Craft's also gone. If your background is a craftsman, write it in. Both are effective skill point sinks that the 4e fighter doesn't have to worry about.
So the 3e fighter then has the chance to put points in Handle Animal, unlike his 4e counterpart. In reply the 4e fighter can pick Streetwise (a mix of Knowledge (Local) and Gather Information), Endurance, and/or Heal.
In terms of what you can buy out of the box the 4e fighter is therefore a long way ahead, mostly due to the consolidation of the skill list (climb, jump, and swim being separate skills for someone with so few skill points is crippling). But the 4e fighter can easily broaden his skills beyond that list. He can add a skill to his list (or get a +2 in a skill) with a background. He can get a whole new skill not on that list with a feat. And most importantly there are the multiclass feats. Feats that give you a decent bonus
and give you a free trained skill from the class list of the class you are multiclassing into. Picking up e.g. Arcana, Nature, or Perception is therefore easy - and I don't think I've ever seen a fighter with fewer than four trained skills. And given that this normally includes Athletics and Perception (the first worth three skills in 3.X, and the second being Spot and Listen) you're into ranger skill territory.
A 3.X fighter struggles to get skills not on that list without ceasing to be a fighter for a while - he's paying 2 for 1.
And for an illustration of how skilled you can make a 4e fighter I've thrown a 1st level human fighter wielding a pair of shortswords together just now designed to be a skill monkey. He's perfectly legal and has the following skills trained:
Perception, Athletics, Streetwise, Intimidate, Stealth, Thievery.
(Sneak of Shadows and Twilight Adept feats, and a background to slip perception onto the skill list).
In 3.X terms that equates to the following skills trained:
Spot, Listen, Search, Jump, Climb, Swim, Gather Information, Knowledge (Local), Intimidate, Hide, Move Silently, Open Lock, Disable Device, Sleight of Hand.
14 skills in 3.X terms. 14 skills, all of which, without exception, are useful to a rogue. A 3.X
rogue would have immense problems matching this level of ability (and that without the hiding bonus from Twilight Adept).
So yeah. Tell me how the 4e fighter isn't better at skills than the 3.X fighter when the basic fighter can get climb, jump, and swim as one skill, and a properly built fighter who's trying for skill versatility can challenge a 3.X rogue at being a rogue
And before you suggest I nerfed my combat potential to do it, the answer is that my stats are all in good places for a fighter (there's a good reason to have a dex of 15 or higher with a fighter, and wis adds to your opportunity attacks as a fighter) and of my two feats, one gives me a 2d6 sneak attack 1/fight - well worth a feat.
It's a class feature for the Thief.