I think its important to focus on the purpose of stats in rpgs. This is a bid of a rant so feel free to disagree on any point.
"Everyone is different, no two people are not on fire" -- Strongbad
The primary purpose of stats is to make characters with unique strengths and weakeness with in the context of a uniform set of rules. This point really frustrates me, several rpgs end up with characters that are all the same. In my opinion this leads to boring characters and doesn't promote strategy.
"Only certain kids get prizes" - Homestar junior announcer
Yes, you get prizes for fighting and sometimes your stats change. But this can be dangerous if it stuffs up the first point. You need to make sure to perserve the strengths and weakeness of each character. Nothing annoys me more than suddenly realising that all the characters in my party have become generic plate wearing spell casters with infinitely excellent swords of doom.
"FL? Far-off lands,Foreign Leadership Camp,Fish Lake." - Homestar
STR, DEX, WIS, CHR, SPD, HP. All nice in theory but what do they all mean!?? I'm a firm believer that simplicity is the key to a computer rpg. If stats become to complex then the player doesn't care about them. As gain more of characters then I start caring less and less.. especially if there are a lot of stats.
Knights of the Old. Great game. Used d20. I only ever bothered with the main characters stats and upgrades and levels.. all the others I just clicked 'auto-level'. With all the stats, feats and skills and information.. it was hard to care about more than one character, that's why personally I think OGL or d20 is a terrible system for multiple character RPGs (it wasn't exactly designed for it.) Its far too bloated.
"Trevor I pine for you" - Strong Bad
I ran out of quotes that applied. Anywho! The tricky part is balance, which was your original statement. I think rpg difficultly tends to balance itself. A clever player will figure out strategies to get around the weakeness of there characters. A patent player will level up their characters through level grinding, that will give them an easier time of it.
Before fighting a large boss, give the player a dungeon mobs to work on. Before facing a tough dungeon give the player world mobs or some kind of training ground or lower area they can go to if they need something to grind.
If you tend towards hard but possible, the player can always make it easier for themselves if they need to. Leveling your characters to level 99 is nice, but killing the final boss with level 40 characters is even cooler.