A long time ago when talking about the holy trinity of MMO's I suggested a form of balancing the "light and fast" hero against the "heavy tank" hero that wouldn't take away from either one's ability to do damage and such. The idea was simple in that it was simply one hero would do 1/2 the damage of the other, but in exchange would - on average - hit twice as often. On paper, this makes both characters balanced. They will both, on average, do the same amount of damage over a span of time. However, this type of mechanic would fail for another reason. Lack of Fun Factor.
The Curse of the RNG
One of the favorite quotes I've ever read, and I can't remember the source aside from a book called "Improbable", is about low probability events. The quote reads: the only thing you need to know about low probability events is that sometimes shit happens. In other words, at some point in time a low probability event happens. If something is a one in a million shot of happening, then it isn't that surprising if it happens provided it is only once in a million. As long as you can be relatively sure the same thing isn't happening in one of the other 999,999 possible chances it has at this given moment, it isn't that weird that it is happening, right?
Now, take this and apply it to games and RPGs. If you've been gaming long enough you've seen it. The total party wipe because the party keeps rolling very low on their attack checks. The complete rofl stomp of a hard/perilous/impossible event because the party keeps rolling very high on their attack checks. These are both low probability events happening. It is highly unlikely for one player to roll a nat 20 critical strike on all five of their attacks in a given round, but I've seen it happen - twice in the same game. It is highly unlikely for a player to roll 5 natural 1s in a row and thus condemn their 20 dexterity elven archer to death when they trip - without having moved - during an attack. But I've seen that happen too. The point is, shit happens.
It's Fun When You Hit...
So now, let's take a look back at our two fighters. Let's call them Hammer and Dagger. Hammer hits twice as hard but has 50% of the to hit chance that Dagger has. Dagger has the inverse of Hammer's attack/damage stats. Can you see the problem forming? There are a few of them.
For one, if Hammer gets an unlucky streak it is very likely he will do nothing in the current fight. He is useles dead weight. This won't feel very good to him, and in a lot of ways can make it nigh impossible for him to fight an NPC built like Dagger because the fast/nimble character is going to be harder to hit. Dagger can, with a bit of luck, whittle Hammer down. However, I can hear some of you saying that Hammer knew this when he signed up for the role. To those folks I ask what happens when Hammer gets lucky?
Suddenly, Hammer is hitting every attack. He destroys the fight, whallops the bad guys, and gets to be the hero. That's awesome, right? Well, not if you're Dagger. As Dagger you specifically traded off your ability to do damage for your ability to hit people. However, a hot streak of the dice and Hammer is both hitting and doing damage.
Being Powerless Sucks...
The easy fix to this problem is to get rid of some of the other staples of RPGs. Make it so that a nat20 doesn't always hit. Now you have people that Hammer just can't hit, and people that Dagger just can't hurt. The problem here lies in the fact that now that character is useless. they are powerless in the fight, and that isn't fun at all. Any time a player's character is incapable of acting in a useful/meaningful way, that player is actively not having fun. The longer this goes on - and in a table top RPG a single round can take an hour with a large enough group - the less fun it is.
Interstingly enough different types of games have different solutions to this. "Old School" games, and those built in their ilk - i.e. the current 40k crop of games - would probably just say to suck it up and deal. But then, there is a reason that a certain kind of gamer - the challenge addicts and number crunchers to over generalize - are the ones who feel the strongest pull to that kind of a game. Other games would likely try to either over complicate things to balance it out further, or otherwise build in mechanics to help make sure everyone gets their chance to shin. Access to different stunts/abilities for one, or just the ability to excel at different kind of tests for another.
The point of this post isn't necessarily to solve a problem with a very simple approach to balancing two classes, but rather to point out where the problems can come in from. How things that seem simple and easy at first can come up against some very serious problems with a little bit more analysis and some real world application. No one cares about the fact that they rolled 6 20s in a row last session when this session they can't stop throwing 1s and 3s. At the end of the night they're just going to remember that they didn't have as much fun this night, and if you're lucky, that it was random chance and not something else that got in the way.