Basement ceilings can require a different plan
Lower ceilings, soffits, mechanical access panels and patched areas can make basement work more detailed than an open room upstairs. Ask how the contractor will deal with edges around vents, bulkheads and recessed lighting, and whether those details are included in the quoted area.
If the ceiling has cracks or movement lines, ask whether the proposed repair is cosmetic or intended to address a recurring joint problem. Removing texture alone will not stop a crack from returning.
Price the endpoint, not the demolition step
Request a scope that identifies protection, texture removal or covering, drywall repairs, skim coating, sanding, primer, paint and cleanup. When comparing bids, check whether all companies are promising the same final surface.
For unknown older texture, discuss testing before disturbance. If the ceiling is already painted, let the contractor know because paint can affect how easily the texture releases.