Responsive design is definitely easier to design and is easier to implement. This is why it's by far the preferred method for creating and designing a website.
However, it will allow less control over the design of each screen. On simple websites, it looks pretty straightforward, but on heavy and complex websites, it tends to be a real headache—components that don't work on mobile (advertisements) or visual hierarchy can become non-user-friendly. Sometimes Responsive websites have an unfinished feel, and elements seem to be arranged in a way that just seems to fit the screen, but is not designed for the best user experience. However, there is another approach, which is mobile first. This basically starts your design on a mobile and builds up to the desktop. But it still doesn't resolve the problem.
Another advantage of mobile first is speed. Research shows that companies with an Adaptive website will often perform better on loading-speed tests than a Responsive website...