Main reason for using an app: often you get features not available on a website. For example The Guardian app allows me to read through today's paper serially (or did when I had it) which I like, rather than requiring me to find and select articles.

Reason for not using an app: you can avoid advertising! This also speeds it up hugely and avoids ad-borne malware (such as is currently plageing a forum I use). And you can suppress tracking to some extent - this browser blocks all Google ads for example.

On security and privacy either could be better. I trust and understand Firefox. I would trust the NYT and WashPo apps (but they probably require a subscription). I wouldn't trust some others. Secure programming requires care and effort - and a policy and procedures to ensure it. I can't imagine some publishers prioritising that.

Mostly I use a browser and reject apps.