I vote more skills and more combat power, particularly at higher levels.
For skills, I prefer a suggestion I saw on these boards some time ago, which was to give the Fighter a "noncombat specialty".
I don't remember the details of the original work-up, just the concept, which I thought was pretty neat.
A Fighter still wouldn't be a skill-monkey, but there's be some room to accomodate different character concepts without the necessity of looking beyond the class.
If it was left to me, I'd do it something like this:
A fighter would select a noncombat specialty at 1st level.
At 1st level and at every odd level thereafter, the fighter would receive a bonus skill rank in each of two skills chosen from those available to his specialty.
Each specialty could include three (or so) skills, as per the examples below:
Sentinel: Listen, Search, Spot
Acrobat: Balance, Jump, Tumbling
Cavalier: Handle Animal, KS: Nobility & Royalty, Ride
To avoid straightjacketing the character later in his career, you could allow the option of switching specialties at certain levels to enforce some consistency while allowing room for organic development.
As for combat power, I think the fighter is fine if you're only using the PHB + PHB2 and making the comparison against other "meat shield" classes, but underpowered as compared to the ToB classes, high level spellcasters, or splatbook-tweaked Clerics and Druids.
Personally, I llike the idea of bonus damage dice.
Double the bonus damage dice for a single attack made as a full attack action to discourage all the dice rolling from iterative attacks, but let it also apply to extra attacks from cleaves, whirlwind attacks, etc.
By 20th, the bonus could be something like +4d6/+3d6/+2d6/+1d6 for iterative attacks, or +20d6 for a single attack (taken as a full attack action).
The bonus damage dice either wouldn't apply to extra TWF attacks, or it would be a matter of splitting the damage dice. Either way, the TWF character wouldn't benefit disproportionately.
I'm not sure how much bonus damage would be appropriate, though.