There isn’t a definitive, “canon” answer, because they’re from different authors, written to excel in different ways. But you can compare what each is *portrayed* as being smartest at:

## Sherlock Holmes (Conan Doyle)
**Type of intelligence:** analytic + observational + scientific  
- Extraordinary at rapid inference from tiny physical details (mud, ash, calluses, footprints, handwriting).  
- Strong breadth in chemistry, forensics, and practical investigation—often solves cases by *building evidence* and testing hypotheses.  
- Tends to be fastest when the problem is grounded in physical clues and real-world mechanics.

**Limits (as portrayed):** can be overconfident, sometimes bored by “mundane” cases, and his success often depends on having access to scenes, traces, and legwork.

## Hercule Poirot (Agatha Christie)
**Type of intelligence:** psychological + logical + social  
- Famous for “the little grey cells”: reconstructing events from inconsistencies in stories, motives, relationships, and human behavior.  
- Often solves cases with minimal physical evidence—by interviewing, spotting contradictions, and understanding character.  
- Especially strong in closed-circle mysteries where everyone has something to hide.

**Limits (as portrayed):** less focused on physical detection than Holmes; more reliant on conversation, timing, and social insight.

## So who’s “smarter”?
- **If “smarter” means better at forensic-style deduction from physical minutiae:** **Holmes** usually wins.  
- **If “smarter” means better at reading people, motives, and unraveling social deception with sparse evidence:** **Poirot** often wins.  
- **Overall:** they’re written as peak geniuses in different domains—Holmes as the ultimate *detective-scientist*, Poirot as the ultimate *psychologist-logician*.

If you tell me what kind of problem you mean (e.g., a modern murder investigation, a locked-room mystery, a con artist, a missing-person case), I can give a more specific head-to-head.
