Careers Future Prospects After Contract Employment

For the past 3.5 years I'm working in a small software development organization. Recently I got an offer with TCS for 6 lpa and another offer with a small company which is providing contract employees for Verizon (8.5 lpa). I'm very confused about accepting second offer, since they are claiming I'm a permanent employee with them but they are going to send me to Verizon as a contract employee. Will it affect my career's future prospects. Some people are telling me that I won't get any permanent employment in future if I worked as a contract employee in India. Please help me.

There is not much difference between an contract role or a full-time employee if you are in technical career path, your career trajectory will depend upon the technology used, your role and type of project : support, maintenance, pure development etc... including the domain for which IT service is provided
check on these factors and decide accordingly your friends in BA/ PM roles can clear your doubts rather than posting in HR forums.