So I played 4e for the first time today
what happened to fighters being better at fighting than wizards?
They still are. THAC0/BAB equivalent is always the same; +1 per 2 levels. However, a fighter will have several advantages over the wizard:
1) Fighters gain a +1 bonus to either single-handed or two-handed weapons (depending on the particular fighter).
2) Fighters gain a +2 or +3 bonus to using any weapon they are proficient with (which is all but exotic weapons). Wizards have much worse weapon proficiencies. (A wizard using a dagger gets the +3 bonus, but that's a lot less damage than a fighter, and a rogue gets a a special +1 bonus on top of that while using a dagger.)
3) Fighters boost their Strength, wizards do not.
A 2nd-level wizard using a dagger with a Strength of 10 will have an attack bonus of +4 and deal 1d4 damage.
A 2nd-level fighter with a bastard sword and a Strength of 18 (quite likely, as now even dwarves can get a +2 bonus to Strength) will have an attack bonus of +8 and deal 1d10+4 damage, assuming they're using the weapon in one hand and haven't taken the Weapon Focus feat for additional damage (and that's a weird assumption).
4) Fighters have slightly more hit points, much higher AC and many more healing surges per day. (They also heal more when targeted by healing powers or even when using Second Wind.)
oh, and the healing surges DO NOT replace a cleric, learned that the hard way
(may the dwarf's soul rest in peace, his axe now in the hands of the half-elf)
Yes. Clerics are still useful, and since they heal as minor actions, it means the cleric isn't losing a whole lot of action when someone gets wounded.