I believe using a responsive website is better than using a mobile one.
It is a cost-effective solution. Often, site-owners tend to design a separate website for mobile devices instead of optimizing their existing website. This, however, creates confusion for both users as well as the owner. It is ideal to redesign your existing website using a dynamic layout that is rendered properly in both desktop and mobile devices. After all, a website with a uniform URL is easier and less expensive to maintain than having multiple.
Also, scalability is an important feature when it comes to a responsive website. While designing, you have to keep in mind that the screen of a mobile is smaller than a desktop. The elements should be arranged in a way that the user does not face any problem while exploring the site.
Having a separate mobile website will also be very exhausting from a testing point of view. You will need more resources, time and bandwidth!