In the last few years, we've all heard the same argument about which Joker on screen is the true Joker as we know him from DC Comics. The truth is, none of them are; not Romero, Nicholson, Ledger or even Mark Hamill and I'm betting that Leto will fall short in some way as well. This isn't because I don't like any of their looks, the writing, or their acting styles or any such subjective nonsense as that. It's just tough to play crazy.
To put this in perspective, we need to boil it down to who the Joker is from the comics, his source material. Some folks may not realize, but the Joker has never actually even had an official origin story, which is a rarity for such an established character. That, in and of itself, should tell you what we're dealing with here. By every conceivable definition, the Joker is clinically insane. He is well known to change his own history upon recounting in order to meet whatever end he desires, whether it be fear, sympathy or anything in between. He's not a man who lives by absolutes, his personality and tactics change with the swiftness and violence of an enraged gorilla. Can you imagine many actors outside of maybe Daniel Day-Lewis who could get into that headspace long enough to play for even a half-hour episode of a cartoon, much less the months it would take to film a feature-length film? It may be quite difficult for anyone not suffering from (or enjoying, in his case) clinical insanity to actually step into such an utterly fractured psyche for any length of time and remain in relatively good mental health.
Let's take a quick look at the actors involved, leaving out Leto, since Suicide Squad hasn't yet been released. First, we have Cesar Romero from the 60's era Batman TV show, who was basically just a clown-themed criminal in grease paint. This is a representation of the Joker's early years where he was really just going for crimes with a humorous slant. In 1989's Batman film, was more of the egotistical madman with a gift for crime and a flair for the dramatic. He was intelligent, to a point, had a temper and narcissistic tendencies. The closest we got to the true Joker, was indeed Mark Hamill as his voice in the 90's era Batman Animated Series. He was clever, funny, full of himself, played coy very well, had his flair for the dramatic, a quick temper and occasional lust if not love for Harley Quinn. He both hated and loved Batman in his own twisted way. Because it was a cartoon, however, it never caught his sadistic and homicidal nature. It also never ventured into his truly anti-social/anarchistic side. This, though, was what Heath Ledger captured best in his portrayal of the Clown Prince of Crime. He was at times gleefully murderous and somewhat Machiavellian in the details of his plans.
If you were to wrap all of these into a wonderfully twisted, murderous package, you would get the Joker that Bill Finger, Bob Kane and Jerry Robinson created way back in his first appearance in 1940's Batman #1. This was what has been built up for the last 75 years of his existence in the medium of comic books. It's why nobody has ever fully captured his madness. The Joker is an agent of chaos, anarchy personified in a sadistic, comical and dangerously bipolar package. He's not the sort of villain that believes himself to be the hero, as is often a trope found in literature and film. He's also unafraid of death, as long as it makes a good punch line. This is also a complete and utter sociopath, who wants nothing more than to see everyone and everything suffer and get a good laugh out of it. His "relationship" with Harley Quinn is simply hedonism, a way of satisfying his needs at her emotional expense, which further underlines his sociopathic ways. He's a man who hates everything, if he even has that capacity. More accurately, he doesn't have emotional attachment of any kind to anyone or anything. That's something I've never seen an actor be able to pull off convincingly, and if I'm wrong, then I somehow doubt they'd also be able to deliver on the rest of the character's *ahem* "unique" personality(ies?) as well.
Everyone can argue their version of the Joker until they're blue in the face, but the only one that matters, that ever really will, is the Joker in the pages of DC Comics publications. That, however is just my opinion. You're welcome to take it or leave it.