I think it's pretty well impossible to convert a 1e or 2e character into a "balanced" 3e character for the simple reason of character wealth. Nowadays it's very integrated into the balance of the game, but back in the day an easy way to make a low-level character viable within a higher-level group was to give them a few powerful magic items.
It isn't just exceptional strength that needs fixin' when converting old school characters.
HOWEVER- I feel that balance is secondary to preserving a campaign's integrity. So what if there's no way a 10th level character in 3e should have a vorpal sword? If the character you played for FIVE YEARS (real time) got one in 2e, and just barely hit 10th level, he should keep it... he earned it!
Now, that doesn't mean that he should expect to see it never get targeted by a disintigrate, turned into green slime, shattered, sundered, etc.... but it shouldn't be arbitrarily taken away cuz it doesn't fit the wealth guidelines.
In similar vein, a fighter with an 18(00) strength really ought to be stronger than a 2e psionicist with an 18 strength once they're both converted. It's only fair; it was one of his advantages. And really, if converted characters are tougher than 'standard' 3e pcs of their level, all that means is you can throw tougher challenges at them.
For example, how many 2e characters fought and slew a marilith by 10th level?
How many 3e characters have?
You see my point... 2e characters were practically legendary MUCH earlier than 3e characters are. Epic level came around 1oth-14th, imo... when everyone reaches "name level" (old school concept there!)
It's really, really hard to do a fair conversion. My advice: don't mix 2e pcs with 3e pcs until the converted 2e pcs have had a chance to "equalize" over time, i.e. until they've leveled up enought to justify their magic items or lost a bunch of them due to attrition or whatever.