A major advantage that dedicated servers have over the others is Maximum performance. There is no conflicts for resources so all your resources are dedicated to your server like the name suggests. This is particularly important if you have a complex website which requires lots of processing power. The same principle applies if you have a site which attracts a vast number of visitors. The best way to ensure the smooth running of such a website would be to move away from shared hosting.
A dedicated server also gives you more flexibility. You will be the only one using your particular server, you'll have the freedom to expand and grow your site as and when required. Nearly all successful websites reach a point where expansion becomes inevitable, and when this happens, they automatically need more bandwidth. With shared hosting, this is quite often not possible since the servers are already operating at full capacity.
They also give you more security and reliability. Reputable dedicated hosting providers normally own and maintain various data centers, which house these servers. As these systems are delicate such a facility should have the required attributes such as a dependable power supply, with stand-by generators at hand in case of outages, superior climate controls like appropriate cooling, and a safe data connection network. It should also possess the best equipment available, and a team of experienced technicians at hand to ensure that any unforeseen eventuality can be rectified on time, with minimum losses to their clients