First of all, the reputation of the company does not guarantee anything. It doesn't increase your chances of geting H1 or labor or I-140 or GC. The only thing good about the reputated company is that there will be work to show that you will actually be working with them, and they have enough work throughtout your employement. 

It is true that they can initiate your labor based on future employement. The labor is what determines how much you should be paid once you get your GC. Now the thing is, T.Mahindra being a big company will have that ability to pay the prevailing wage (labor) at the time of filing based on future employement. While an indian consultancy will not have that ability based on the tax return so they won't be able to file for future employment and so need you to join so they can use the pay stubs and net income to justify the ability to pay during your I-140 process. 

Now coming to the point of joining T.Mahindra, You have to check if your current contract with your current company that forbids you to join the vendor generally up to a year to two, and other part is that if the contract mentions you will have to be with the company for certain amount of time. You have to be careful here, as the current employer can sue both you and tech.mahindra on this case for breach of contracts, and i've seen the decision on favor of IT companies.

Joing T.Mahindra would definitely would definitely bring better opportunities for you, but do make sure they keep up with their words, and try to get that in writing that they will initiate your GC process and also take care of the legal fees if such condition arises.. Thats the best way I think.

Good Luck!!