Not that Marvel hasn't tried; far from it. Over the years, Marvel has put forth a litany of characters that try to invoke the same ideas of Batman - without sinking into the murky waters of copyright infringement - with little success.
So of the minor successes, who is the Marvel analogue for Batman? Let's take a look at the top candidates:
Moon Knight (Post-werewolf hunter beginnings and Pre-current crazy Bendis makeover) has oft been considered the man to beat when it comes to Bat-Analogues. I'll admit that it's a pretty easy case to make when you take a glance at the character: He's highly trained, works at night, has tons of gadgets, and has a rich alter ego. Hell, he even has a crazy, murderous ex-sidekick.
However, once you dig a little bit deeper, the whole thing starts to fall apart. Even before his recent schizophrenic turn, Moonie wasn't the most sane of heroes. Donning up to three different alter egos in a manner that would make Stanislavski proud, he probably did more to scare his closest friends than his deadliest enemies. Further more, he has a penchant for being a little overly violent, like when he cut the face off of Bushman a few years back. I know Bats has done some extreme things in the past, but he tends to stop short of physical mutilation.
In the end, Moon Knight is more akin to the 90s AzBats everyone hates than he is the Bruce Wayne Batman everyone likes.
Pros: Night-themed, lots of Gadgets, Rich.
Cons: Crazy, Overly Violent.
Percentage Batman: 85%
The Shroud is definitely the dark horse on the list. Created in 1975, He's a blind, mystically-augmented, cape-wearing vigilante that one the surface doesn't seem like he'd be similar to The Bat. In a twist from Moon Knight, as you dig deeper into the character, the more similar to Batman he becomes.
Tell me when this sounds familiar: Ten year old rich kid, Maximillian Coleridge, is orphaned when his parents are killed in front of him by a common criminal. From there he devotes his life to justice, studying criminology while keeping his body in peak form. In an attempt to take one further step into awesome crimefighterhood, he travels to the east to work with some monks... who end up blinding him to unlock his mystic potential.
Now, blind, he's able to access a mystic extrasensory perception that allows him to see everything around him at once - Kinda like Daredevil, but without the radioactivity.
Since then, he's gained the ability to access a darkforce dimension that allows him to teleport wherever he wants to be. So, yeah, that kinda puts him in the 'definitely not Batman' camp. However, given his look and his origin, I couldn't not put him on the list. He's the analogue for when DC finally goes crazy and gives Batman powers, which I'm sure they'll do at some point...
Pros: Traumatized by Parents Murder, devoted life to Justice, got special training from Monks...
Cons: ...Those monks blinded him. Also he has mystic powers.
Percentage Batman: 65%
In a way, Nighthawk was literally created to be a Bat-Knockoff. In another way, he's the farthest thing from it. Put on your comics hat, things are about to become confusing.
Okay, so as a fun not-crossover-crossover, Roy Thomas created a JLA Analogue to fight the Avengers called the Squadron Supreme. The team was comprised of a superstrong flying guy (Hyperion), a super fast runner (The Whizzer), a man possessed with an otherworldly stone that gave him energy powers (Doctor Spectrum), and a regular human vigilante (Nighthawk). Simple enough, right? Wrong. That team came from an entirely different dimension that only occasionally, never permanently.
The version of Nighthawk running around the Marvel Universe right now was first recruited by the villainous Gamesmaster to be an evil version of his alternate dimension persona. After a brief flirtation with being the bad guy, Nighthawk came to the side of the angels becoming a charter member of The Defenders. Still with me?
So, convolutedness aside, it's Nighthawk's alter ego that makes him like Batman. As Kyle Richardson, Nighthawk runs a multi-national corporation that gives him the resources to fight crime that would make anyone jealous (except probably Moon Knight because he's got his own cash flow). More recently, Kyle's given up the mantle of Nighthawk to Joaquin Pennysworth in a move similar to Bruce giving up the mantle of the Bat to Dick Grayson. So he's like a Batman Incorporated Bruce Wayne now, without the galavanting the world and making out with a Catwoman analogue.
Pros: Literally created to be a knockoff Batman. Rich. Runs a company.
Cons: Was briefly evil. Crazy convoluted origin.
Percentage Batman: 73%
The more I think about it, there's only one answer to this question. There's only one character in the Marvel Universe with a history of taking down enemies way more powerful than them, someone with deep ties to supergroups both big and small, has at least one dead sidekick in their past, and dresses like a rodent.
That's right, Marvel's Batman is none other than Squirrel Girl.
And she would totally kick Batman's ass.