Since the days of Sherlock Holmes, society has been enchanted by brilliant detectives, able to uncover the crimes and methods of those who would subvert and lie about the law. This has given rise to almost super-heroic detective characters like Bruce Wayne or L Lawliet, better known by their aliases Batman and L.
While DC and Death Note are both full of compelling mysteries, those central detectives investigate, solve and deal with crimes in very different ways. However, which detective is better at their job?
Technological and Underground Resources
Batman has some of the most broad-reaching resources of any fictional detective ever. On top of the numerous gadgets he keeps in his pouches, he has access to advanced computers and hacking equipment that allows him to access data banks all over the world. He has an advanced understanding of chemistry, which allows him to uncover oddities about chemicals left on crime scenes. He can record conversations happening across Gotham, and once created a gun that could literally kill the impossibly powerful Darkseid.
By contrast, L has advanced computer skills, but nothing outside the realm of real-world plausibility. He gains information through an underground network he accesses via Watari and other "abnormal" sources of information. While Batman will often use advanced technology to confirm his suspicions, L uses more limited resources to get what he needs.
Most often, L just watches what happens, examines the data and moves forward with what often turns out to be the best possible strategy. Ultimately, Batman does something similar, but his technology supplements and further refines his conclusions. While L can gain information through underground channels, both Bruce Wayne and Batman have enough contacts throughout every echelon of society to learn information that could prove essential to cracking their mysteries.
L works wonders with far less, but ultimately it's Batman who has the superior resources. He can do everything L can, and more.
Use of Police Resources
Batman has access to the Gotham Police Department, while L often works alongside detectives already working on a given case, be they Naomi Misora or the Kira Task Force. However, while Batman often forms friendships with police officers, like Commissioner Gordon, L essentially appropriates police forces and assigns himself as their leader, using them to further his own investigation directly.
The key difference is this: the police and Batman are separate entities pooling resources together, while L just takes what he needs and uses them like pawns. This often places L's officers in dangerous, sometimes lethal positions. L doesn't like seeing his officers die, but Batman will put himself in danger to protect people like Commissioner Gordon or Renee Montoya.
L used the deaths of Naomi and later Ukita to determine key details about the crime. While the nature of Kira's power made it impossible for L to protect them -- Naomi's death was a complete shock -- he didn't exactly make an effort to protect his police officers either. This goes even further when L convinces Light's father to potentially put himself in harm's way to confirm neither Light nor Misa are Kira. L forces Light's father to threaten to murder the two. If the two had their memories of being Kira, they could have killed him. However, L forced the three into the traumatizing situation with almost sociopathic calmness.
It might be unethical, but it gets results. Points here go to L.
Investigation vs Trickery
When Batman investigates a crime scene or criminal, he often approaches it like a forensic scene, looking for physical evidence and using profiling to figure out which known criminals might have been involved. He accesses the situation much like any other detective would, just with advanced resources and contacts.
L, on top of analyzing data available, will often just manipulate people into revealing key details about their methods or motives on the spot. A perfect encapsulation of this is how he figures out where Kira is. He looks at which country the first suspicious deaths of criminals by heart attack took place, then plays a broadcast region-by-region to lure Kira into exposing himself. This manipulation of information forces the enemy to play their hand, resulting in the criminals offering L the key information.
This means that L can solve a crime that doesn't leave any physical evidence, like with the Death Note. Where Batman would look for physical evidence that does not exist, L can subvert all expectations. The point here goes to L.
Bringing Criminals to Justice
Batman has little difficulty enforcing justice in Gotham thanks to all of the above combined with his world-class martial arts abilities. While his villains might not always stay imprisoned, Batman still pretty much always solves the crime and gets to the truth. He's an effective and efficient crime fighter who generally brings evildoers to justice.
By contrast, L does bring one Kira to justice, but he fails to apprehend the remaining two. Although he does figure out who they are, he can't actually prove they did the crime. While L has a lot of fantastic accomplishments and solved many crimes in the past, he doesn't always succeed, and in Death Note his failure is a big one.
While L is a great detective, Batman's track record in actually settling cases is superior in every way. Ultimately, Batman is the better detective.