Sherlock Holmes vs Light Yagami

Holmes comes to Tokyo to solve the Kira case. Light reads of his arrival the night prior, but does not know Sherlock's name. Can Sherlock catch him, or will Light take Sherlock's potato chip and eat it?

Which iteration of Sherlock?

The original. He must be able to discover Light and prove beyond a doubt he solved the crime, and Light must do everything in his power to stop him.

I haven't read the novels, so I'm no use here. Sorry!

Everyone who has read them and seen the others say the originals superior.

One major issue which unless pardoned in the OP gives Light the win: Unlike L, Sherlock would refuse anything supernatural. While he'd normally get to Light faster than L, the supernatural ties will clash with Sherlock making it difficult to link certain points together or even finalize things.