A material-only figure is not a complete installed project price. Before comparing totals, check whether both options cover the same rooms and services. Flooring quantities, existing material removal, preparation, furniture handling and trim can all change what the proposal represents. None should be assumed to be included merely because installation appears in the description.
Ask for a clear explanation of the work rather than an unsupported promise of the lowest price. If one proposal costs less, identify why: a different product, less finishing work or a different assumption about preparation may be involved. A fair comparison starts with equivalent scope and an understanding of any unresolved conditions.