If you see the same job on an employer website and a job board, which way should you go with your application?

Apply through the company website with your CV and follow up with an email or phone call to make sure they’ve got your application.
A direct application allows you to talk about a genuine interest in the employer which is usually hidden on a job board. The phone call makes sure they see your application as plenty end up in junk email and never get seen.
The job board may well have scraped the vacancy page of the company (they do this to increase the number of roles on the board) or it could be an agency working for the employer, and you don’t want to apply twice
You may not realise this but some Job Boards reformat your CV really badly and recruiters/employers get to see a pretty poor version of the CV you’ve prepared.