Have they supplied complete assembly drawings with the housing held at the proposed grip? Without that, how are they defining the load rather than just repeating the part weight?
Ask for the complete loaded mass, centre of gravity and inertia information for each identified assembly, with the proposed motion for the responsible assessor. The different grip depths matter to that comparison, not just to whether the housing fits between the fingers.
Then give the second supplier the intended adapter information and get its assessed assembly and price updated. Or have it propose the complete tool. Don't compare its incomplete load claim with the first supplier's eventual full assessment.