If you ask CIO/CTO's whether it is better to contract a large software engineering company than a smaller one (staff wise), most would reply that it is less of a business risk to contract the larger company.  Their reasons would typically be that larger organisations have more resources, more stability due to its size, better experience and have a better chance of delivering the project on time and within budget

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We disagree. Experience has shown us that larger organisations are actually more of a risk than smaller companies. A large company would assign a limited amount of resources to your project.  In many cases said resources would be shared between their various clients.  Resources of larger companies are usually not as loyal as resources of a smaller company - less ownership implies less attachment. Therefore they leave more easily for better pastures. This creates fluctuations in the ability for the team to implement your project. Unless you are the contracted company's largest client, you will not be treated as you deserve to be. A small company values your business more.  Resources are more attached to the company and work harder to make the company a success, implying they will take better care of you.  They have less incentive to leave for other opportunities because they are employed not for the money, but for helping realise the vision of that company.  

There is something magical about small companies when it comes to their ability to serve your needs.