(1) Do you have lot data spread across your in-house systems such as ERP, CRM, other softwares?
If high amounts of data is spread across multiple in-house systems such as ERP,CRM and other softwares which can be potentially integrated to the Contract Management Software, it is beneficial to have an on-premise contract management system rather than a cloud system where integrations can be limited to other softwares that you are already using.
(2) Do you have the hardware and licenses to run the contract management software in-house?
All Contract Management Software's require essential hardware/software licenses, review this ahead of time to ensure that all costs are planned.

(3) How much security the Contract Management Software provides when it runs in cloud?
Good Contract Management Software deploys best of the breed security techniques including two factor/multi-factor authentication (MFA) features.
http://www.contractexperience.com/resources/choosing-between-cloud-or-on-premise-contract-management.html