To start with a VPS is always better. You can always upgrade to a dedicated server when you need additional resources. A lot of other factors like resource-heavy website, OS requirement, managed services, cost, etc come into account when deciding which is better.
@mihirthakur Your signature sends HD users to a web hosting provider. Why do you ask the question "Which is best for a medium scale organization Vps or Dedicated Server?", what is the purpose of this question?
Don't you know which of those is better option for yourself? I don't get it.
The major difference that lies between both the hosting is the space that you have for your website to get hosted which indirectly or directly creates a major impact on the performance of the website. Dedicated Server provides you the entire space wherein VPS provides you imaginary boundaries to host different websites on a single server. VPS is definitely good for small and medium websites and Dedicated Servers are recommended for larger websites.
You can always start with vps before move to dedicated server. It will reduce cost and it will give idea about which configuration to choose if you are moving to dedicated server once traffic gets high.
I would recommand to start with a VPS or a cloud offer, so you can have flexibility for your infrastucture.
When you have defined your needs in ressources, you may consider switching to a dedicated physical server
For a medium scale organisation, VPS can prove best server. Since, Dedicated servers are almost always very expensive. It is generally a good idea to start with the VPS servers as long as your company is not generating enough revenue to reinforce the cost of a dedicated server.
I think the main difference between VPS and dedicated hosting is the independent environment. Though on VPS you get virtual environment for your website but you need to share the server with others. In dedicated servers, you are the whole and sole owner of the server.
In my opinion it basically boils down to if you want to hire people or not and how much you want to outsource instead. You can get some good size VPS solutions and it is still a good choice for anyone who doesn't want the time and expense of maintaining their own hardware. In my own company I handle the design work, web development, programing, sales and support. That's why I can offer Tier 3 support which many companies can't promise because they put hirelings behind the phone.
Since you have a medium scale organization VPS would be a great option to manage your server. As you do not have to fall into hassle of managing server and also don't need to invest on a tech savvy staff memeber.