For all the people who constantly say that the Joker is only considered a dangerous villain because Batman refuses to kill him, you might want to note that this goes both ways; the Joker doesn't want to kill Batman, either, and passed up several opportunities to do it. Therefore, it's not a one-sided deal; due to their odd, symbiotic sort of relationship, neither wants to kill the others. This is also why the Joker, obsessed with Batman, likes to play around with him attempting to drive him nuts; it was more than once that either luck or the Joker's unwillingness saved Batman.
In addition, the Joker has no special emotions towards the Punisher; he will not play around with him and toy him. The Joker is EXTREMELY intelligent, and I find it extremely unlikely that Frank can just sneak in somewhere and shoot him without the Joker finding out somehow; not saying that can't happen, because if the Punisher jumps him and snipes him, the Joker will die; but that's equivalent to a one-sided prep match, which this is not.
However, if this is a prep fight (two-sided), the Joker can take this. He's smarter than Frank, and is more than likely to be able to get him inside a trap and proceed to own him using Joker Venom, a gun, or some other form of elaborate weapon.
An arena match? Well, if both have their regular weapons- the Joker with his guns, knives, and gadgets, and Frank with his guns and other skills, I suppose Frank can take it a long range; he's a better shot than the Joker and also has the advantage of body armor. The Joker, however, has incredible pain tolerance; in his proper form, he can laugh and shrug off basic pain. If they close in, though, Frank's life just gets a whole lot more miserable. Not saying that the Joker is necessarily going to take this, but Frank- while a skilled hand-to-hand combatant- isn't as good as Batman in that department. The Joker had, on several occasions, used bursts of strength in combat (his insanity grants him occasional somewhat superhuman strength while in combat), and Batman has- more than once- commented on the Joker's speed, and he is clearly depicted to be agile. His weaponry is very effective- joy buzzer, for example, can be lethal in close-ranged combat, and his acid-squirting flower can damage Frank. Joker Venom can also come into effect.
Conclusion? Both are very skilled. Frank can take a one-sided prep match, like FascistCrusader says by simply sniping the Joker, the Joker can take a two-sided prep fight, and an arena fight is more interesting to analyze.