It shouldn't matter too much, but if you have to ask, then I would recommend you keep it as one application for now.

Keeping it as one application is simpler.

• It works out of the box
• All required dependencies are there
• Axios is already set up to get the token
• Laravel mix can compile it for you

With two applications, you have to...

• Set up a Vue app and its dependencies
• Work through a stateless API, like Ehsan Fazeli said
• Switch between two apps

The only time using two applications might be viable is when you have two teams, one version control, and people keep getting their branches crossed.

I think it really depends on how you've designed your architecture and how your application's ends speak to each other. If you're building your backend as a stateless API, then there's no need for your backend to be right beside your frontend.