Building your website on a shared server means that your pages may be affected by a neighboring site that devours too many server resources. For example, if that site receives a huge spike in traffic, your pages might load slowly—or not at all. Investing in a dedicated server greatly reduces this potential problem, plus it gives system administrators greater control over the apps and scripts that they can install on the server, too. Shared hosting is far more limited when it comes to what you're allowed to do, because everything you do could potentially affect the other sites with which you share the server. When you've got the server all to yourself, your scripts and apps won't impinge on anyone else's bandwidth or RAM.
With dedicated servers, you want a lot of storage and power if you are building an enterprise website. Otherwise, you may not need as much storage. There are also differences between processors. With single processor servers, you will not spend as much, but if you are purchasing a server with multi-core such as an Intel Xeon processor, then you will likely spend to have that additional power.