Responsive over non-responsive web design.

Responsive website are just better than non-responsive ones. They are better for the user and they are better for the developer. A responsive site is able to function appropriately on all types of screen sizes. It provides a sensible layout on mobile and desktop while also providing a similar experience on both devices. While for the developer they are cheaper, require less maintenance and provide better UX through progressive enhancement.

Responsive sites require less work and a shorter development cycle. Developing a responsive site will often take less time than developing two sites. With separate sites, there may have to be a lot of code duplication if there are similar areas. There may have to be two separate designs. There will have to be two separate code reviews. Everything to do with non-responsive sites takes so much longer. Secondly, some users may want to use the desktop version of the site instead of the mobile site. Therefore the developer will have to include a way to for the user to do this. This overhead leads to development taking longer. With responsive sites, all of this is taken away. Plus, if you are using a CSS framework the majority of the work around actually making the site responsive is taken away.

CSS Frameworks makes building responsive sites even easier!

Having two sites will allow you to give a rich experience to desktop and mobile users. You will be able to craft exactly what you want on each site. This is great if there were only two screen sizes but that’s sadly not the case. You will not be able to do this for tablets or devices with medium or extra-large screens. Building a responsive site allows you to cater for any size screen. A responsive site allows you to change the layout on many different screen sizes. You can fiddle with breakpoints to make your content align to various screen sizes. This means every user will get an optimal experience on any screen device.

An optimal experience at every device size

Once you have created the site you then need to think about site maintenance. Choosing two sites could mean having two design teams or having two development teams. You need to coordinate changes with these two teams to make sure everything is consistent. If you are getting data from a back-end and there are changes to the back-end you will need to change both sites. With a responsive site, you only make changes in one place. A responsive site can mean that changes are made quickly and there is less management to worry about. It allows you to be more agile, fix bugs quicker and release features at a faster rate. 
Finally, you should consider the user experience when moving from the desktop site to the mobile one. Having two sites means you can make a dedicated mobile site but it might be quite different from the desktop version. With a responsive site both versions will be quite similar. If there are significant differences this might confuse the user. They might be put off from using the site. Progressive enhancement can provide a seamless transition from mobile to desktop which the user will appreciate. And, crucially, it could mean that the users return to the website.

UX is everything. Source.

User experience, maintenance and workload are all important when developing a website. You want to maximize UX while minimizing maintenance and workload. I think that only responsive websites offer this. They allow you to focus on building and releasing features quickly. Whereas, non-responsive sites require much more care and thought to build two consistent sites.