I love Batman. Lots of people do. But he's hard to talk about because there are, like, thirty seven different Batmen depending upon which media you're absorbing, which writer is at the helm, the needs of that particular story and so many other things. Elements of character (Anger, calculation, paternal instincts, striving for human contact) and capability (Detective, martial artist, gadgeteer, icon of fear, iron will, long term planner) shift around based on the specific vision, and the particulars of the title that he's in. The Batman who patrols the streets of Gotham and the Batman who fights alongside Superman in the JLA are so different as to be almost unrecognizable. Almost. Somehow, they're all still Batman, and that's a testimony to the power of the character.
This introduces an interesting and long-established challenge in gaming - how to mechanically represent Batman. Part of the interest of this problem is that it's very easy to model any particular Batman, even the JLA one, but very difficult to model all of them. If JLA batman were unleashed on the streets of Gotham, those would make for some very boring stories because he'd outclass the challenges so quickly as to perhaps be funny, at least for a little while. Similarly, Gotham Batman isn't going to last long on Apokolips.
The easiest solution is to fragment up the "levels" of play, so that street-level Batman simply has a different set of stats than JLA level Batman. Unfortunately, people seem uncomfortable with this sort of approach, because it's a bit too meta for taste.
Another option is to try to point balance things so that Batman really is as tough as other JLA'ers, at least on paper. The old DC Heroes game did this and, to be frank, it was pretty crazily broken since it managed it through what can only be described as an arbitrary and capricious pricing structure. The net result was a Batman who was technically "balanced" (ish) with Superman by using a build you would never, ever see in play.
If you want a really fiddly solution, you can make it all about resource management. Batman has a ton of 2 point tokens, Superman has a dozen 10 point ones. When faced with almost any problem, Superman can overcome it by spending a token, but that's maybe not smart if it's a small problem. In contrast, batman needs to spend a LOT of tokens (like 16 of them) to get a 10 point effect, so it's not cost effective for him to do the big whammies. So Batman uses his tokens to deal with small menaces (though he can combine them when he must) and makes sure Superman has the "budget" to deal with the real problems. 
The last simple option is to make up the difference in narrative control. If it costs 20 "points" to make Batman in your system, but 100 to make Superman, then you hand Batman's player 80 points worth of narrative control, usually in the form of something like Fate Points. Now Batman has the ability to make declarations and manipulate events with the explanation being that he "planned for it". When he's not playing at that level, his Fate Point supply falls down to the appropriate budget (so maybe it's a 40 point gap when he's with the Outsiders, and no gap at all at the street level).
This actually works pretty well on paper, but in practice it depends a lot on how the Fate Point economy works. If Batman has only a few more Fate Points than Superman, or Superman can earn them just as easily as Batman, then they stop being a unique point of distinction for Batman.
Thankfully, this a solvable problem. I mean, I can't tell you what the solution is because it depends on the game. For example, the Refresh mechanic in the Dresden Files RPG addresses a similar problem to this, but it does it on an abbreviated scale. The difference between a 10 refresh character and a 1 refresh character is noticeable, but it's no Batman vs. Superman. But even it can break down depending on how the game is played. In a game with stingy rewards, high refresh is very potent. In one with generous awards or lots of free tag opportunities, then a difference in refresh doesn't represent much of a handicap. This is one of those things that's going to be determined from table to table, from session to session, and it's very hard to come up with hard and fast rules for how to handle it.
The solution I find myself toying with is also allowing those "normal" characters more bang for their buck, so that Batman not only gets more Fate Points, he can do more with them. This might be generic (like the list of effects or bonuses gets bigger and longer) or they could be bought (like superpowers) to do specific, schtick supporting things.
The former approach is, I think, pretty self explanatory; the latter is trickier. It runs the risk of looking a lot like Batman has a different character sheet at "JLA Tier", so that needs to be accounted for. While a bit ham-fisted, they could be explicitly called out as functions of the tier, not the character, but that's not terribly satisfying.
More effective, I think, would be some way to build these things so they scale up while supporting the same schtick, so the type of effect remains the same, but the scope of it changes with the scope of the game. Take, for example, Batman being the greatest detective in the world. At the street level that lets him do all kinds of Sherlock Holmes stuff, but at the JLA level, that Sherlock Holmes stuff scales up to things like outsmarting alien god minds, and making plans that unfold over millennia. . At street level, his icy glare can make a gangster back down. At the JLA level, it can cow the warlord of a thousand worlds. All because he's just that awesome
What I like about this approach is that it allows you to support the other human-but-awesome characters. If you go with a generic system (where they all just get more fate points, or generically more useful fate points) then the difference between Batman and Green Arrow becomes one of schtick, not mechanics, because when you're operating at Superman's level, it really doesn't matter if that attack came from a bow or a batarang,
With unique "narrative powers", you can call out Green Arrow's schtick so that he can, for example, spend a fate point to create a situation where there's a tiny target that needs to be hit to great effect. "Great effect" might mean blowing up a car (at street level) but it might mean killing a sun (at JLA level). As I think about it, this works incredibly well for gadgets. Street gadgets might include a mini blowtorch and some flash bombs. Super Or higher level gadget start getting much sillier (though one of the nice things about not-superfriends Batman is they keep the gadgets toned down these days. I dig that.)
It'll be worth thinking some about what these things-to-be-named later look like. It's easy to come up without he first dozen or so, but it may take some kicking around before I'm convinced this is a sustainable idea.
As a final nod, twitter shout out to @semiocity, @boymonster, @ThadeousC , @johnoghue and others whose discussion drove me to this post, which was quite different in its intent when it started.
1 - I love Superman too, but this is not the time for that particular geek dialectic.
2- And about 6 different Bruce Waynes, just for good measure.
3 - For those only passingly familiar, here's the issue in a nutshell. The JLA has guys like Superman, Green Lantern, Wonder Woman and The Flash. Batman is smart and tough and fast, but he's still a normal guy, so those really only go so far. So given that, how does Batman keep from being utterly useless when fighting villains who are dangerous enough to threaten the whole Justice League? Historically (think Superfriends, if that means anything to you) it was by making him a gadget guy, to the point where his utility belt probably outclassed Green Lantern's ring as an item of power. Modern writers have concentrated more on the tactical and planning advantages of havign the World's Greatest Detective on the team, and Grant Morrison's JLA run cemented Batman as a chessmaster, the guy who wins because he's always several moves ahead of any opposition.
4 - Pricing skills in a supers game is tricky, but it gets really crazy when they're treated like they're on par with powers. If Martial Arts are more expensive than Heat Vision, you may have a problem.
5- Entirely impractical, I know, but it's an interesting thought experiment. Consider, for examine, that many other JLA-ers may have 8 point tokens.
6 - Short form: The more magic you have, the fewer fate points you begin a session with.
7 - Which is why we don't depend on refresh as the *sole* balancing mechanic.
8 - Oh, god, as soon as I said that, I broke out in hives. That's a horrible, fight-picking name. It desperately needs to be called something else. I mean, in FATE terms they're a particular flavor of stunts, but that's not an answer. Aspect stunts? Might make sense in Fate terms that these stunts need to be tied to a specific aspect, like "Greatest detective in the world" or "Master Archer"
9 - Yeah, as an aside, the Archer power is not to be more accurate, but rather to create situations where being accurate matters.