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1. who is the greater detective

2. who is overall smarter

That is some realistic art in the first pic.
I'd give both scenarios to Bruce.

In both cases, Bruce. Why? While both characters are fictional, one is a comic book (primarily) character and the other is not. Generally speaking - not always, but generally - the comic book character will tend to have higher stats in (almost) any area. Bruce, as a detective, is almost omniscient. He deciphers things that are, at times, not even of this world (be it extraterrestrial or supernatural). He uses technology that doesn't exist in the real world (or in fiction more closely aligned with the real world). He's planning has allowed him, a mortal, to cater for virtually any eventuality (including not only death, but times pans across thousands of years ...the story that had Plastic Man scattered as atoms in the bottom of the ocean ...can't remember the name at present).

Finally, note that the reason he's in the JLA is not because he's wealthy or he knows martial arts or he's 'scary' ....it is solely because of his mind. A human being present in a club populated by beings such as Firestorm, Captain Atom, Superman, Martian Manhunter and other creatures that are frightful monsters (note: monsters. If those beings existed in real life they'd be monstrous nightmares. Imagine something like the Martian Manhunter, who could sniff out every thought you have, has super strength and speed, can shapeshift into any evil thing he wants, can be invisible behind you, or intangible beneath you, we're not sure what he eats apart from a like for Oreos and MEAT, can plant thoughts in your mind, etc) ....and don't get me started with Superman. I fully understand Lex Luthor's need to destroy the being ...note, the being as Superman is not a man.

Anyway, Bruce is simply operating at a higher level of intellect than (nearly) any non-comic/manga/cartoon character. This includes Sherlock by the way.

^^^Huh.
I just thought Bruce was cooler.

Bruce Wayne wins...