There are about 4.61 billion mobile and tablet users in 2016, the count is increasing by the year a study shows that by 2019 the number of mobile users will reach 5.7 billion. There are two ways to design a website to be compatible with mobile devices, one is the responsive web design and the other is design specific to suit a mobile device. Here is an infographic about Responsive Design Vs Mobile Site Design.
Many parameters are to be considered to finalize a design. It depends on- the budget of the company for developing a website, user experience, technology developments, and further opportunities. Plan your website strategically and take a wise call according to the requirements.