Here are the some advantages and disadvantages

Advantages:

Consistent branding and user experience. Because a responsive website is one website that adapts to all different devices, all the information is available through the same user journey on all devices (and optimised for screen size). To explain this a bit further, a visitor on a desktop computer could enter your website and find the used Ford Fiesta page. They could then return later in the day on their mobile device, and because they will be looking at the same website they will be able to find the same page using the same steps. In addition, the look and feel will be the same, helping to support your branding.

Optimised for SEO. Responsive web design is officially Google best practise. Because of this they prefer this approach, and can regard responsive websites better than those that aren’t mobile friendly. This can directly affect how well your website shows up in search results when people are “Googling” on a mobile device.
Simpler maintenance. Because you don’t need to update the main site and then the mobile site, one change will update the content across everything. This is generally easier for your team if you use a content management system, or for your web design agency. Either way, it makes it a lot easier to stay on top of content and keep track of what’s been changed.

Doesn’t redirect visitors to a separate mobile website. Redirections like this can be read negatively by Google, and can also slow the time taken for visitors to find the information they want.

Disadvantages:

The very best websites have been designed specifically to be responsive – from layout to buttons and everything in-between. Whilst we can (and have) updated existing websites to become responsive, the ideal solution is to re-design, so that the site can perform at the best possible level.
There are arguments to be made about whether visitors really NEED to be able to access the full website content. If you’re on a mobile, are you looking for certain information only? The only way to really tell is to use a program like Google Analytics to see how visitors to your standard site, on a mobile device, navigate the website. What do they look for and where do they go?